Automatic Generation of Software Components for Real Options Modelling
Automatic Generation of Software Components for Real Options Modelling
A.Chortaras,Y.Guo,M.M.Ghanem
Department of Computing
Imperial College London
{ac901,yg,mmg}@https://www.wendangku.net/doc/479491522.html,
Abstract
This paper describes the design and implementation of a software sys-tem that,from a high level speci?cation language,generates source code
for the valuation of real options.The speci?cation language allows the de-
scription at an abstract level and independently of any valuation method
speci?c details,?rstly of the?exibility that is present in an investment
project in the form of a collection of individual real options,and secondly
of the dynamics of the underlying stochastic state variables.The dynam-
ics of the state variables are assumed to be continuous di?usion processes.
From these speci?cations the system generates e?cient and reusable soft-
ware components,which are subsequently combined with software compo-
nents that implement numerical methods in order for the?nal real option
valuation code to be generated.The system aims at facilitating the rapid
development of real options pricing applications and improving manage-
ment’s ability to perform?exible project analysis under di?erent project
structures and stochastic model assumptions.
1Introduction
The development of the real options approach to capital budgeting originates from the inability of the traditional discounted cash?ow techniques to properly capture managerial?exibility to review decisions in the future depending on the (favourable or unfavourable)market developments[22]1.
From a computational point of view,the solution to the problem of valu-ating the?exibility embedded in an investment project using the real options approach involves three basic steps.The?rst step consists of identifying the ?exibility itself and the underlying stochastic state variables and modelling it as a collection of one or more interacting real options contingent on these vari-ables2.The second step is to de?ne a speci?c stochastic model that describes the behaviour of the underlying state variables.The?nal step,by combining the previous information,is to derive a mathematical formula or to construct a computational procedure from which the value of the?exibility can be calcu-lated.
1The literature on real options theory and its applications is large and[20],[22]provide a comprehensive guide to it.
2A set of interacting real options is described as a collection in[23].
Identifying the collection of real options that a project may include and of their underlyings is a task of the management team.For modelling the dynamics of the underlying state variables simple stochastic models(mainly geometric Brownian motion)are frequently used because they lead to equations that can be solved or approximated analytically.However,their ability to provide a realistic description of the actual behaviour of a project’s sources of uncertainty is limited.In many cases,in order for more accurate estimations to be obtained, more complex models have to be used.This fact,combined with the complexity of the interactions among the several options that a project may include,often makes the use of numerical techniques the only tractable way to calculate the value of real options.
Valuation Code
Stochastic Model
Figure1:System Diagram.
However,developing code for the valuation of individual or of collections of real options,in combination with di?erent stochastic models is an expensive, error prone and time-consuming procedure.Automating this process has several advantages.A software system capable of valuating with minimum program-ming e?ort the?exibility embedded in new investment projects for di?erent possible project structures and stochastic models can be a valuable risk man-agement tool.It can help the e?cient and rapid design of the investment plans of the management by shortening development time,reducing implementation costs of other project-speci?c valuation models and o?ering increased?exibility in the analysis of the projects.
The requirements for such a system can be summarized as follows:
?Ease of speci?cation of new investment projects and of the real options that the management identi?es in them.
?Ease of description of the sources of uncertainty that a?ect the value of a project,and?exibility in the speci?cation of custom stochastic models.
?Generation from these speci?cations of computationally e?cient valuation software.
?Extensibility and use of transparent valuation technology.
This paper discusses the design and implementation of an automatic software generation system whose objective is to meet the above requirements.The sys-tem is essentially a problem solving environment and its structure is illustrated in Figure1.Its inputs are?rstly the description of the?exibility of investment projects in the form of interacting individual real options,and secondly stochas-tic models that describe the dynamics of the underlying state variables.The outputs are software components that e?ectively model these speci?cations and which,combined with appropriate numerical method software components,can be used for the computation of the value of the real options.
Both inputs are given in the form of documents written in a high level lan-guage,keeping thereby at a high level the interaction with the end-user.Ana-lyzing the documents,the system automatically generates software components that are reusable,so that they can be used again for the valuation of the same (e.g under di?erent project or model assumptions)or future projects.The gen-erated components correspond to object-oriented classes,build upon abstract class hierarchies that capture the structure of the real options and stochastic models.
1.1Related Work
Authors in[3]and[4]present a similar prototype system,which models?nancial options and allows the e?cient development of?nancial options pricing appli-cations.The only other problem solving environment in the?nancial domain that uses software synthesis is the system presented in[13].It uses a high level problem speci?cation language and computationally is based on the?nite dif-ferences method.In the?eld of real option valuation there exist several either stand-alone or spreadsheet-based commercial applications.They mainly use the lattice methods to compute the value of the real options and they are usually in?exible in specifying stochastic models di?erent than the geometric Brownian motion for the underlying state variables.
The system that we present in this paper is an extension of the system in [3].It incorporates several of the features that real option valuation techniques require and applies the software synthesis technology to real option valuation.
In brief,the main di?erences between valuating?nancial and real options from a computational point of view,are the non-completeness of the market environment that usually holds in the case of?nancial options,the possibility to de?ne collections of interacting real options,and the use of more complex stochastic models for describing the underlying state variables.Thus,in com-parison with the system in[3],in our system we extend the support of the underlying?nancial market environment to allow for market incompleteness and we incorporate the capability of modelling and valuating collections of real options,while we maintain the in-built?exibility of the original system to handle complex stochastic models.In addition,we use exclusively the XML language as the language through which the valuation problem speci?cations are provided to the system.The use of XML-based languages in the context of?nancial applications has already been proposed with FpML being the most signi?cant among these proposals[10].
The structure of the rest of the paper is as follows:In Section2we discuss
the classi?cation of real options and the valuation techniques.In Section3 we describe the design and the overall architecture of the system.Sections4 and5provide implementation details about the way in which real options and uncertainty sources respectively are modelled and represented in the system. Section6presents the computational part of the system with a discussion on the use and implementation of numerical methods.Section7provides some examples of the use of the system,and Section8concludes the paper o?ering some suggestions for future work.
2Real Options Classi?cation and Valuation
The real options approach to capital budgeting equates the value of the man-agerial?exibility with an option premium,in a way that if such a?exibility exists the net present value of an investment project is equal to its traditional net present value(without the?exibility)plus the option premium,i.e.the value of the real option.
Under certain assumptions(see[22]for details)the value of a real option may be calculated by appropriately applying the methodology developed for pricing ?nancial options.The analogy between real and?nancial options although close is not exact and[22]provides an extensive discussion of this analogy and its limitations.In the same source and in[19]the analogy between the terminology used in?nancial and the real options can also be found.
2.1Simple and Interacting Real Options
Simple real options,i.e.real options that describe a single type of?exibility independently,without taking into account the possible simultaneous existence of other types of?exibility,have been studied extensively and lie at the basis of the standard classi?cation of real options.They are contingent only on the stochastic state variables of the market and similarly to the?nancial options they are completely de?ned by their payo?functions and the type of their exercise style(i.e.whether they are of European or American style).
A standard classi?cation of simple real options is presented in[22].It in-cludes the option to defer an investment decision,the option to expand or to contract the scale of a project by undertaking or forgoing future investments,the option to temporarily shut down production,the option to abandon a project for a salvage value and the option to switch use.All of them are de?ned in a way similar to the standard?nancial put or call options.
As an example of a simple option we can consider a company that undertakes the project of constructing a production unit of a new product.If the acceptance of the new product by the market is better than expected,the management may later wish to expand the production unit at the cost of an additional investment outlay.The value of the?exibility to expand the production unit F can be modelled as the value of a standard put option with payo?max(eV?I,0)where I is the additional outlay,V the value of the project and e the scale at which the expansion will increase the value of the project.According to the real options approach the expanded net present value of the project is NP V E=NP V T+F, where NP V T is the net present value of the project without the?exibility to expand it.
However,usually investment projects are more complex and cannot be e?ec-tively modelled using a single simple option.The managerial?exibility present in real investments may then be expressed as a collection of several,interacting among them,real options.A simple case of interaction is the simultaneous pres-ence of two or more mutually exclusive real options,for instance of the options to expand or to contract the scale of a project.In other cases,interacting real options can be modelled as a sequence of compound simple options.In such cases an earlier option is contingent not only on the value of the state variables but also on the value of the subsequent options.Thus,the exercise of an earlier option a?ects the exercise possibilities of the future options.For example,if the management has the?exibility to expand the scale of a project and subse-quently to contract it if the market environment deteriorate,the payo?of the option to expand may be expressed as R+max(eV?I,0)where R is the value of subsequent option to contract the project[23].
2.2Option Valuation and Numerical Techniques
The valuation of both?nancial and real options is based on a mathematical framework,whose purpose is to e?ciently describe the stochastic behaviour of the market state variables that act as underlying assets for the options.In this standard framework the dynamics of the state variables are assumed to be con-tinuous It?o di?usion processes.The full details of the mathematical framework on which our system is based,which is an extended version of the standard framework,is presented in Appendix A.In short,it allows the de?nition of continuous multi-factor stochastic models with stochastic dividend structures and it accounts for market incompleteness.
The selection of an appropriate stochastic model and the estimation of its parameters is one of the major problems in real options valuation.Di?erent models have di?erent implications for the value of an investment project.Due to their mathematical tractability usually simple models are used,the speci?cation, however,of a‘good’stochastic model for a project is the object of a lot of research activity.
The value of simple real options may be calculated directly from equations A.1,A.2or A.3,A.4.For the cases where no analytical solutions are available, several numerical methods may be used,most of which are extensions of the ?nancial options pricing methods.In general,they can be divided in?nite di?erences methods(introduced by[5]),Monte Carlo methods(introduced by [2])and lattice methods(introduced by[8]).The approach that these methods take is essentially di?erent.Finite di?erences methods attack directly the partial di?erential equation,while Monte Carlo methods work by simulating the paths that the stochastic variables https://www.wendangku.net/doc/479491522.html,ttice methods,which are widely used in real options valuation,are very simple to implement,however they have the disadvantage of being easily applicable only when a geometric Brownian motion is assumed for the underlying processes.[17]and[6]discuss how lattice methods can be used as discrete time approximations of more general processes.
Interactions among real options make in general their values non-additive, not allowing therefore the straightforward application of the standard valuation formulas developed for?nancial options(see[23]for a detailed discussion on the possible interactions and how the total value is a?ected).Appropriate valuation techniques that account for the e?ects of possible interactions must be used.[23]
proposes such an extension of the lattice method,while[12]describes how Monte Carlo simulation methods may be applied when several options are embedded in a project.
3System Design
The architecture of the system re?ects its objective to produce real options valuation code in a systematic,?exible and transparent way,by interacting at a high level with the end-user.It o?ers the user the possibility to easily de?ne collections of interacting real options and custom stochastic models for the underlying state variables and the?exibility to combine them with numerical methods in order to obtain the desired valuation code.
The system deploys the technologies of automatic code generation,software components and XML language.Its kernel is implemented in Java while the product of the automatic code generation are software components implemented as C++classes.The generation of C++code o?ers maximal computational ef-?ciency.The use of the software components technology facilitates the mapping of?nancial and mathematical concepts to software entities at a high level of abstraction,and o?ers reusability of the generated code.The components have a well-de?ned external interface that speci?es the operations that they support and their data members.The XML language is used as the means through which the user provides to the system the speci?cations of the real option valu-ation problems.Its use increases the?exibility and extensibility of the system, while it keeps hidden from the user any low level programming details.
The functionality of the system is based upon the basic steps of the real option valuation procedure presented in the introduction.It consists of three parts,which are graphically illustrated in Figure2.More speci?cally these parts are:
?The option speci?cation part,whose task is to generate the software com-ponents that represent real options and collections of real options.Two types of components are generated by this part:the individual real option and the real option collection components.The speci?cations of the real options are provided to the system in the form of XML documents.
?The stochastic model speci?cation part.Its task is to generate the stochas-tic model software components,which represent stochastic models describ-ing the dynamics of the underlying state variables.Similarly to the option speci?cation part,the speci?cations of the stochastic models have the form of XML documents.
?The valuation code generation part,which generates the?nal real option valuation software component,by combining components generated by the previous parts with an appropriate numerical method.Numerical methods are also implemented as software components.The appropriateness of a particular numerical method component for being used for the solution of a speci?c valuation problem depends on the mathematical characteristics of the problem and on the solving power of the algorithm that the numerical method component implements.
Figure2:System architecture.
The set of di?erent real options and stochastic models that the XML lan-guage that we use in the system allows to be de?ned determines the scope of the system.On the other hand the number of the available numerical method components determines its power3.
The individual real option components represent di?erent types of manage-rial?exibility.Typical examples are the options to abandon,to expand or to contract an investment.The external interface of the components is created by using the technique of inheriting from abstract software classes that model the structure and the permitted operations of real options at an abstract level. This interface allows the numerical method components to interact with the real option components independently of any real option-speci?c details.Real option collection components represent sets of individual real options that have a speci?c order and type of interaction.
The stochastic model components represent de?nitions of stochastic pro-cesses.Similarly to the real option components,an external interface is de?ned
3For a problem solving environment scope denotes the extent of the problem set that it can address,while power refers to its ability to solve the posed problems[11].
for the interaction with the numerical method components in a stochastic model-independent way.The necessary mathematical manipulation of the stochastic models such as symbolic transformations and derivation of pricing equations in our system is done using the symbolic algebra system Mathematica.
The valuation components are the?nal product of the system and those that perform the actual real option valuation.They have the form of C++classes with a well de?ned external interface so that project valuation applications based on them can easily be developed.
The numerical method components that the valuation components use have the form of C++templates.The collection of numerical method components forms a numerical library.This library is extensible so that new numerical methods components implementing di?erent numerical methods may be added. Addition of new numerical methods components capable of solving more of the problems that can be posed by the real options and stochastic model speci?ca-tion parts increases the power of the system.
The software components that are produced from each part are reusable and can be seen as constituting libraries of real options and stochastic models.This implies that di?erent real option collection components may be combined with di?erent stochastic model components in order to produce several valuation components.This provides the user the?exibility to test the e?ects that di?er-ent valuation models imply for the same investment project.Moreover,a real option collection component is a collection of already existing individual real option components.If the constituent parts of the collection(i.e.the individual real options)are already available there is no need to generate them again.In general,if some of the desired components have already been generated not all three steps need to be undertaken in order to generate a new valuation com-ponent.Thus,there is a certain form of functionality independence among the three parts of the system.
If compared with the system presented in[3]at the architectural level our system follows a very similar approach.However,there are signi?cant di?er-ences in the functionality and implementation of its subsystems.The real option speci?cation part replaces the?nancial domain level modelling part and o?ers the system its real option modelling capability.The numerical method com-ponent library is modi?ed so as to permit the valuation of collections of real options.Finally,the stochastic model speci?cation part is based on the more ?exible mathematical framework of Appendix A.
4Real Options Speci?cation
The purpose of the option speci?cation part of the system is,?rstly to provide an abstract,high level way of specifying individual real options and real option collections,and secondly to generate from these abstract speci?cations con-crete software components suitable for use by the valuation components.The reusability of the generated components is achieved by keeping both the speci-?cations and their structure independent of any stochastic model and valuation method-dependent details.
4.1Speci?cation Documents
In this section we present the XML-based real option speci?cation language through whose use individual real options and real option collections can be de?ned.For each speci?cation document the real options speci?cation part of the system generates the corresponding software component.The software components are essentially concrete subclasses of the abstract class hierarchies that we describe in the following section.
The complete speci?cation of a real option is achieved by creating two di?er-ent types of XML documents:the individual real options speci?cation document and the real option collection speci?cation document.
The?rst document type contains all the stochastic model and valuation method-independent properties of an individual real option.As such it provides to the system complete information about the sources of the option’s value uncertainty,the payo?function of the option and the time at which the option may be undertaken.It supports the de?nition of both simple and compound options.
Following these requirements we de?ne three basic elements which any indi-vidual real option speci?cation document must contain:
?The var element which de?nes the state variables that are involved in the calculation of the value of the real options.These can be more than one, in which case a multidimensional valuation problem is posed.If available, additional information about the behaviour of the option as the state variables approach zero and in?nity may be also provided by using the lower and upper elements respectively.This information may be used by the valuation components to increase accuracy and speed of convergence.
?The payoff element which de?nes the payo?of the real option as a func-tion of the underlying state variables previously de?ned,possibly of time and of any other parameters,usually in the form of investment outlays.
?The american element through whose use the document speci?es whether there are early exercise possibilities embedded in the real option or not.
The additional element compound may be used in order to de?ne compound options,i.e.in order to specify that the individual real option that the document de?nes is contingent also on the value of a subsequent option or of a subsequent collection of options.If this is the case,the payo?function may use the reserved keyword underlying to refer to that value.
The form of the individual real option speci?cation XML document is demon-strated in Figure3,which presents the speci?cation of a European style option to expand.
Collections of real options are de?ned by creating a real option speci?ca-tion document of the second type.Its purpose is to de?ne sequences of sets of interacting individual real options,that have already been de?ned by the cor-responding individual real option speci?cation documents.It must de?ne the relative order of the sets that compose the sequence and for each set the type of interaction among the individual options it consists of.Two types of inter-action are supported:sets of independent and simultaneous,mutually exclusive options.
e
I
r
Figure3:Individual real option speci?cation document.
The main document element is the set element,which de?nes a set of either independent or simultaneous options.If all the options in a set are simple there is no subsequent set,while if there exits a compound option,the de?nition of the set of options upon whose value it is contingent has to follow.A single real option is modelled as the trivial case of a set containing one option only.
The form of the real option collection speci?cation document is shown in Figure4.The document models a collection that consists of an initial option to defer an investment,followed by two mutually exclusive options,to either expand it or abandon it at a later stage.
Figure4:Real option collection speci?cation document.
4.2Components Structure
The real option software components that are generated from the XML doc-uments can be e?ciently used by the di?erent numerical method components only if they have a common external interface.This is achieved by following the object-oriented programming paradigm and generating them based upon abstract class hierarchies.The classes of these hierarchies de?ne the virtual functions that concrete classes,corresponding to speci?c real options,have to implement.The abstract class hierarchies serve also an additional purpose:they
abstract the structural and semantic similarities and di?erences that di?erent real options have.
We de?ne two basic abstract class hierarchies for describing individual real options.The purpose of the?rst one is to provide a complete description of all the dimension-independent characteristics of an option,where by dimension we mean the number of the stochastic state variables on which the option is contingent.The rest of the information that is dimension-dependent is modelled by the second class hierarchy.
Figure5:Abstract classes modelling individual real options.
The bene?t of providing a separate class hierarchy for the two parts is mainly computational e?ciency.The distinction between options that have a di?erent number of underlyings may not be so important from a theoretical point of view but is essential from the computer modelling and valuation points of view. Incorporating both classi?cations in our class hierarchies we have an e?cient representation of real options from both the semantic and computational points of view.
The dimension-independent properties of an individual option are,?rstly the time points at which it may be exercised,which is equivalent to the time until its expiration and whether it is of European or American style,and secondly whether there exists an interaction with other options that can be described at an individual level.As we discussed in Section2.1compound interaction is the most common such relation.It may be described by including in the de?nition of the option class of another data member which represents the value of the subsequent option or set of options upon whose value the option is contingent. The dimension-dependent properties are the number of state variables on which the option is contingent and,as a consequence,its payo?function.
Following the type of options supported by the XML speci?cation docu-ments,in our implementation the dimension-independent hierarchy consists of a root class representing a generic real option,with two abstract subclasses:one representing a simple and one representing a compound option.The dimension-dependent hierarchy consists of a root class with one abstract subclass for op-tions of di?erent dimensions.These class hierarchies are extensible and new abstract classes that support di?erent structures of real option can be added. Concrete real option classes have to multiply inherit from both abstract class hierarchies and provide the implementation of the virtual functions as well as
of any other option-speci?c de?nitions.
In order to model collections of real options we de?ne a similar abstract class hierarchy.The root class represents a generic set of options and has three abstract subclasses:one representing a single option,one a set of independent options,and one a set of mutually exclusive options.The classes contain ap-propriate data members that represent the members of the set,the value of the set and the set upon which they are possibly contingent.
In this way real option collections components consisting of several successive sets of options may very easily be generated.In e?ect,each concrete set class has to inherit from the appropriate superclass,de?ne the individual real options that are its members,and the subsequent set on whose value the set in contingent, if any.This process is performed automatically by the system by analysing the corresponding real option collection speci?cation document.
5Stochastic Model Speci?cation
The stochastic model speci?cation part of the system implements the function-ality of modelling at a mathematical level the dynamics of the state variables on which an investment project is contingent.The user provides a speci?c stochastic model,whose properties must be within the properties of the general mathematical framework presented in Appendix A,and the system generates the corresponding stochastic model software component.The purpose of the stochastic model components is not simply to capture all the mathematical de-tails of the model,but to do it also in a very systematic way so as to facilitate the development of e?cient numerical method components for the solution of the corresponding option valuation problem.
Given that there is no‘best’numerical method for all valuation problems, we design our system without opting for a particular valuation method only. Extensibility and easy integration into it of di?erent numerical methods is pos-sible only if the stochastic model components comply with this requirement.In particular,they have to provide for the numerical method components all the mathematical quantities(in the form of methods that evaluate certain math-ematical expressions)that can be directly derived from the mathematical de-scription of the model and that are needed from the numerical methods.Given the di?erent characteristics that numerical methods may have,the stochastic model components must accommodate di?erent needs.
For example,from Equations A.1,A.2it follows that the price of contin-gent claims,regardless of the speci?c di?usion model that has been selected to model the state variables,satis?es a particular linear parabolic partial di?eren-tial equation subject to certain?nal and boundary conditions.Finite di?erences methods need only the coe?cients of this partial di?erential equation(together with the?nal and boundary conditions)in order to compute the solution.On the other hand,seeing the valuation problem as a computation of discounted expectations,from equations A.3,A.4,A.5it follows that Monte Carlo methods need only the risk-neutral dynamics of the state variables in order to perform the simulation.
5.1Speci?cation Documents
As in the case of specifying real options,a stochastic model in the system is given in the form of an XML document.The document consists of three main parts.
?The?rst part,delimited by the wiener element,de?nes the Wiener pro-cesses that act as sources of randomness in the model.The processes may be correlated.In terms of the mathematical framework of Appendix A this part de?nes the dimensionality of the random sources d and their correlation matrixρ.
?The second part,included inside the assets element,de?nes the state variables of the model.For each one of them appropriately de?ned ele-ments provide a full description of its value and dividend structure dy-namics.This part de?nes the state variables X and the dimensionality of the problem k,the value drift and di?usion functionsμi andσi,and the dividend structure drift and di?usion functionsδi andγi of Appendix
A.For each state variable its state as a traded or not asset must also be
declared.
?If the total number of underlying traded assets is less than the sources of randomness(i.e.if the market is incomplete)the appropriateλi parame-ters must also be de?ned.This information is provided in the third part of the XML document,included within the uncomplete element.
As an example,Figure6shows how the general two factor model for de-scribing commodity prices behaviour presented in[19]may be speci?ed using an XML document.The mathematical representation of the model is the fol-lowing:
dS=αSdt+σ1SdW1
dδ=κ(α?δ)dt+σ2dW2
where the dividend structure for S is dD=δSdt,the market price of risk forδisλ,and the two Wiener processes are correlated with dW1dW2=ρdt.
As we shall discuss in the following section from the speci?cations provided in the XML document the system will compute the risk-neutral dynamics of the state variables,on which the computation of the option value is essentially based.However,if the risk-neutral dynamics are already available they can be provided directly to the system.This may be done by using the rn-assets and rn-var elements instead of the assets and var elements respectively.In this case any information about the dividend structure dynamics and market completeness is not necessary,since it is implicitly included in the risk-neutral dynamics.
5.2Components Structure
The?rst objective of the software components generated from the stochastic model speci?cation documents is to provide in the form of source code,with an external interface,the mathematical details of the stochastic model itself.
Figure6:Stochastic model speci?cation document.
Object-oriented programming and the use of abstract class hierarchies(as in [3])is again how this objective is achieved.Since each stochastic model essen-tially consists of one or more stochastic di?erential equations we de?ne a root abstract class that represents a generic set of stochastic di?erential equations. Its,still abstract,subclasses correspond to problems of di?erent dimensionality, i.e.to problems with di?erent number of state variables.Following the mathe-matical structure of the model these classes de?ne virtual functions for the drift and di?usion coe?cients as well as for the dividend structure drift and di?usion coe?cients for each one of the equations of the model.Given the central role that risk neutral dynamics play in contingent claim valuation,virtual functions for the corresponding risk neutral drift coe?cients of all the state variables are also de?ned.
The next objective of the stochastic model components is to provide code for the valuation of speci?c mathematical quantities that numerical methods need. For instance,in the case of the?nite di?erence methods this corresponds to com-puting the coe?cients of a parabolic partial di?erential equation.Thus,in order to support?nite di?erences methods we de?ne an abstract class that represents a parabolic di?erential equation with the corresponding dimension-dependent abstract subclasses.The classes de?ne the coe?cients of the di?erential equa-tion as virtual functions.
Each concrete stochastic model class has to inherit from both abstract class hierarchies and provide the implementation of the corresponding functions.
Extensibility and inclusion of other valuation methods that need the calcu-lation of di?erent mathematical quantities is possible by de?ning the necessary
abstract class hierarchy that de?nes the method-dependent data structures and the additional virtual functions that concrete subclasses need to implement.The stochastic model component generation part of the system has also to be appro-priately extended so as to include in the generated classes the implementation of the additional functions.
In order to create a concrete stochastic component in the way we just de-scribed,a series of mathematical computations and transformations must be performed on the model that the XML document describes.These include the transformation of the dynamics of the state variables from the objective to the risk-neutral probability measure and the calculation of the coe?cients of the partial di?erential equation.Both steps require several simple algebraic calcu-lations.As we mentioned in Section3in our system the necessary symbolic algebra is performed using Mathematica as the underlying platform.
6Numerical Methods and Valuation
The valuation components are the software components that combine the spec-i?cations of a particular real option valuation problem with an appropriate numerical method,hence they contain the code that eventually computes the value of a real option.
They are implemented as software classes that multiply inherit from the real option collection and stochastic model classes,inheriting thereby all their data and operations.They perform the valuation procedure by properly initializing the relative components and passing into them the values of any real option and stochastic model-related and of any numerical method-related parameters(such as the grid size for?nite di?erences methods or the number of simulations for Monte Carlo methods).
Their most signi?cant part of the valuation components is the numerical method they are based on.Numerical method components may have very dif-ferent structure and computational complexity.They may for example solve a partial di?erential equation or calculate an expectation through simulation.
The valuation components are designed to be used from within external applications.In the simplest case these applications will consist of a few lines of code that initialise and execute them,however more advanced applications that perform more complex risk-measurement operations may also be developed.
In a way very similar to the one described[3]our system supports the use of di?erent numerical methods through a set of software components that consti-tute a numerical methods library.The numerical methods are implemented as C++template classes,instantiated by the valuation component classes.This guarantees the extensibility of the system and the complete distinction between the pure modelling(of both real options and stochastic model)and valuation parts.New numerical components may be added,as long as their implementa-tion is compatible with the other parts of the system.They must be restricted in using the speci?c interface that the real option and stochastic model compo-nents provide.
The existence of a real option and stochastic model for a project is inde-pendent of which speci?c method will?nally be selected for its valuation.The selection depends on several factors.For example,the complexity of the meth-ods that solve the partial di?erential equations and lattice methods increases
exponentially in the dimensionality of the problem,thus in practice they are used only for up to two dimensions.On the other hand,the complexity of the Monte Carlo simulation methods increases only linearly in the number of the underlying factors,being therefore more suitable for multi-factor models.In addition,not all algorithms will be applicable to all problems.For instance, until recently simulation was applicable only on European style options,but [14]proposed a simulation procedure that can be used for American style op-tions.Moreover,computing the value of a set of independent options or a set of mutually exclusive options are di?erent computational procedures.
Although the main purpose of the numerical methods components is the computation of the value of a real option,they may implement a richer func-tionality.For instance,they may perform sensitivity analysis of the several parameters on the project value or compute for which value ranges of the un-derlying state variables and at which time points will the options included in a project be exercised.
In our system currently we have implemented the Cranck-Nicolson implicit ?nite di?erences numerical algorithm component for one-dimensional problems and an ADI(appropriately extending the schema proposed in[15])?nite dif-ferences component for two-dimensional problems.For projects with geometric Brownian motion dynamics we have implemented also the lattice method.The components can calculate the value of mutually exclusive and sequences of com-pound options.Figure6summarises the details of the implemented numerical components.The valuation methodology of these components follows the ap-proaches in[23]and[12].
Method Dimensions Style Interactions Comments Finite Di?erences1,2European Simple
American Compound
Mut.Exclusive
Lattice1European Simple only GBM
American European
Mut.Exclusive
Figure7:Implemented Numerical Method Components.
7Case Studies
This section provides two case studies that demonstrate the functionality of the system.
7.1Option to Develop an Undeveloped Reserve
The purpose of the?rst example is to show how simple real options can be modelled and valuated under di?erent stochastic models.
The example is related with the exploration of natural reserves,which is one of the mayor application?elds of the real options theory.In this example we use the approach in[18],where the detailed presentation and theoretical elaboration of the proposed model may be found.The modelled option is the
option to develop an undeveloped reserve of gas or oil on a tract that has already been explored.The option is modelled as a simple American style call option that has payo?functionΠ(t,X t)=max(X t?I,0).The underlying is the value of the undeveloped reserves X t and I is the investment outlay needed for developing them.
The two XML documents that de?ne the individual real option and the (trivial in this case)real option collection are presented in Figure8.
Figure8:Speci?cation documents of the option to develop an undeveloped reserve.
Following[18]we can assume a geometric Brownian motion dX t=αX t dt+σX t dW with convenience yield dD=δX t dt for the dynamics of the underlying. Figure9presents the XML document that de?nes this stochastic model.
Figure9:Speci?cation document of a geometric Brownian motion.
Providing the documents of Figures8and9as inputs to the system,we get as outputs the corresponding individual real option,real options collection and stochastic model software components.Since the option is contingent on one stochastic variable only,we can combine the previous components with the the one-dimensional?nite di?erences numerical method component to get the?nal valuation component.
The solution that the valuation component computes for the following values of the parameters(taken from[18]):time to expiration T=15,per unit develop-ment cost I=1440,risk-free interest rate r=0.125,current price of developed
reserve X0=1152,volatilityσ=0.142,and convenience yieldδ=0.041is pre-sented in graphical form in Figure10.The solution is computed for a certain grid of values of the underlying and of time.From these values we are interested in the one that corresponds to X=X0and t=0,which is the current value of the option.This value is47.687.
Value
Figure10:Value of the option to develop an undeveloped reserve.
Alternatively,for the valuation of the same real option a stochastic model di?erent than the geometric Brownian motion can be used.We can de?ne for example a mean reverting process dX t=κ(α?log(X t))X t dt+σX t dW with total expected returnμX.Figure11shows the corresponding XML document in which the risk-neutral dynamics of the process are speci?ed directly.
Figure11:Speci?cation document of a mean reverting process.
The system from this document generates a new stochastic model compo-nent,which combined with the already generated real option components and a numerical method component gives a new valuation component.The valuation under the new model may be performed once the estimates for the values of the parameters of the model are available.In the same way other stochastic model components may generated and tested on the same real option components.
7.2Interacting Options
The second example demonstrates how sequences of interacting real options may be speci?ed and valuated.
We consider an investment project in which the management initially has the ?exibility to abandon early the project at some time T1by forgoing a planned outlay I a.If the project is eventually not abandoned,depending on the market conditions,the management at some time T2>T1will have the option to either expand its scale by e for an additional expenditure I e or to contract it by c, saving thereby a capital amount of I c.
Figure12:Speci?cation documents of interacting options.
The options to expand or to contract the scale of the project may be exercised at the same time and they are mutually exclusive.Their respective payo?s are Πe(t,X t)=max(eX t?I e,0)andΠc(t,X t)=max(I c?cX t,0).Since these options follow the option to abandon the project,the option to abandon is contingent on their joint value.If we assume that the option to abandon is
also of European style,following the approach in [23],we can write its payo?as Πa (t,X t )=max(F 2(t,X t )?I a ,0),where F 2(t,X t )represents the joint value of the options to expand and to contract.The total value of the ?exibility of the project is the value F 1(t,X t )of the option to abandon at t =0.
The speci?cation documents for the three individual real options and the collection document that determines their interactions are presented in Figure 12.
If for the dynamics of the underlying we assume a geometric Brownian mo-tion,we can use the stochastic model component already generated in the pre-vious example.
The valuation of the option was performed using the lattice numerical com-ponent for the following values of the parameters:times to expiration T 1=5,T 2=8,expansion percentage e =0.5,contraction percentage c =0.3,capital amounts I e =40,I c =20,I a =50,risk-free interest rate r =0.05,current value of the underlying X 0=100,volatility σ=0.25and convenience yield δ=0.The full results of the computation are illustrated in Figure 13and the value of the option for t =0is 6.3152.80100
200
300Underlying
025
50
75
100
Value
24
6
Time
Figure 13:Value of interacting options.
Having available a set of software components that represent individual op-tions (not restricted to the ones generated in this example)experimentations on the implication that di?erent combinations of them have on the value of the project may easily be performed.The procedure that has to be followed consists of creating the appropriate new collection documents and subsequently combining with a stochastic model and numerical method component,to get the valuation components.
8Conclusions and Future Work
This paper abstracts the computational steps involved in the valuation of real options and based thereon presents the design and implementation of an au-
大数据分析的六大工具介绍
大数据分析的六大工具介绍 2016年12月 一、概述 来自传感器、购买交易记录、网络日志等的大量数据，通常是万亿或EB的大小，如此庞大的数据，寻找一个合适处理工具非常必要，今天我们为大家分学在大数据处理分析过程中六大最好用的工具。 我们的数据来自各个方面，在面对庞大而复杂的大数据，选择一个合适的处理工具显得很有必要，工欲善其事，必须利其器，一个好的工具不仅可以使我们的工作事半功倍，也可以让我们在竞争日益激烈的云计算时代，挖掘大数据价值，及时调整战略方向。 大数据是一个含义广泛的术语，是指数据集，如此庞大而复杂的，他们需要专门设il?的硬件和软件工具进行处理。该数据集通常是万亿或EB的大小。这些数据集收集自各种各样的来源:传感器、气候信息、公开的信息、如杂志、报纸、文章。大数据产生的其他例子包括购买交易记录、网络日志、病历、事监控、视频和图像档案、及大型电子商务。大数据分析是在研究大量的数据的过程中寻找模式, 相关性和其他有用的信息，可以帮助企业更好地适应变化，并做出更明智的决策。 二.第一种工具:Hadoop Hadoop是一个能够对大量数据进行分布式处理的软件框架。但是Hadoop是 以一种可黑、高效、可伸缩的方式进行处理的。Hadoop是可靠的，因为它假设计算元素和存储会失败，因此它维护多个工作数据副本，确保能够针对失败的节点重新分布处理。Hadoop 是高效的，因为它以并行的方式工作，通过并行处理加快处理速度。Hadoop还是可伸缩的，能够处理PB级数据。此外，Hadoop依赖于社区服务器，因此它的成本比较低，任何人都可以使用。
Hadoop是一个能够让用户轻松架构和使用的分布式计算平台。用户可以轻松地 在Hadoop上开发和运行处理海量数据的应用程序。它主要有以下儿个优点: ,高可黑性。Hadoop按位存储和处理数据的能力值得人们信赖。，高扩展性。Hadoop是 在可用的计?算机集簇间分配数据并完成讣算任务 的，这些集簇可以方便地扩展到数以千计的节点中。 ，高效性。Hadoop能够在节点之间动态地移动数据，并保证各个节点的动 态平衡，因此处理速度非常快。 ，高容错性。Hadoop能够自动保存数据的多个副本，并且能够自动将失败 的任务重新分配。 ,Hadoop带有用Java语言编写的框架，因此运行在Linux生产平台上是非 常理想的。Hadoop上的应用程序也可以使用其他语言编写，比如C++。 第二种工具:HPCC HPCC, High Performance Computing and Communications（高性能计?算与通信）的缩写° 1993年，山美国科学、工程、技术联邦协调理事会向国会提交了“重大挑战项 U：高性能计算与通信”的报告，也就是被称为HPCC计划的报告，即美国总统科学战略项U ,其U的是通过加强研究与开发解决一批重要的科学与技术挑战 问题。HPCC是美国实施信息高速公路而上实施的计?划，该计划的实施将耗资百亿 美元，其主要U标要达到:开发可扩展的计算系统及相关软件，以支持太位级网络 传输性能，开发千兆比特网络技术，扩展研究和教育机构及网络连接能力。
最常用生物软件大全介绍讲解
一、基因芯片： 1、基因芯片综合分析软件。 ArrayVision 7.0 一种功能强大的商业版基因芯片分析软件，不仅可以进行图像分析，还可以进行数据处理，方便protocol的管理功能强大，商业版正式版：6900美元。 Arraypro 4.0 Media Cybernetics公司的产品，该公司的gelpro, imagepro一直以精确成为同类产品中的佼佼者，相信arraypro也不会差。 phoretix™ Array Nonlinear Dynamics公司的基因片综 合分析软件。 J-express 挪威Bergen大学编写，是一个用JAVA语言写的应用程序，界面清晰漂亮，用来分析微矩阵（microarray）实验获得的基因表达数据，需要下载安装JAVA运行环境JRE1.2后(5.1M)后，才能运行。 2、基因芯片阅读图像分析软件 ScanAlyze 2.44 ，斯坦福的基因芯片基因芯片阅读软件，进行微矩阵荧光图像分析，包括半自动定义格栅与像素点分析。输出为分隔的文本格式，可很容易地转化为任何数据库。
3、基因芯片数据分析软件 Cluster 斯坦福的对大量微矩阵数据组进行各种簇（Cluster)分析与其它各种处理的软件。 SAM Significance Analysis of Microarrays 的缩写，微矩阵显著性分析软件，EXCEL软件的插件，由Stanford大学编制。4．基因芯片聚类图形显示 TreeView 1.5 斯坦福开发的用来显示Cluster软件分析的图形化结果。现已和Cluster成为了基因芯片处理的标准软件。 FreeView 是基于JAVA语言的系统树生成软件，接收Cluster生成的数据，比Treeview增强了某些功能。 5．基因芯片引物设计 Array Designer 2.00 DNA微矩阵（microarray）软件，批量设计DNA和寡核苷酸引物工具 二、RNA二级结构。 RNA Structure 3.5 RNA Sturcture 根据最小自由能原理，将Zuker的根据RNA
数据分析软件和工具
以下是我在近三年做各类计量和统计分析过程中感受最深的东西，或能对大家有所帮助。当然，它不是ABC的教程，也不是细致的数据分析方法介绍，它只是“总结”和“体会”。由于我所学所做均甚杂，我也不是学统计、数学出身的，故本文没有主线，只有碎片，且文中内容仅为个人观点，许多论断没有数学证明，望统计、计量大牛轻拍。 于我个人而言，所用的数据分析软件包括EXCEL、SPSS、STATA、EVIEWS。在分析前期可以使用EXCEL进行数据清洗、数据结构调整、复杂的新变量计算（包括逻辑计算）；在后期呈现美观的图表时，它的制图制表功能更是无可取代的利器；但需要说明的是，EXCEL毕竟只是办公软件，它的作用大多局限在对数据本身进行的操作，而非复杂的统计和计量分析，而且，当样本量达到“万”以上级别时，EXCEL的运行速度有时会让人抓狂。 SPSS是擅长于处理截面数据的傻瓜统计软件。首先，它是专业的统计软件，对“万”甚至“十万”样本量级别的数据集都能应付自如；其次，它是统计软件而非专业的计量软件，因此它的强项在于数据清洗、描述统计、假设检验（T、F、卡方、方差齐性、正态性、信效度等检验）、多元统计分析（因子、聚类、判别、偏相关等）和一些常用的计量分析（初、中级计量教科书里提到的计量分析基本都能实现），对于复杂的、前沿的计量分析无能为力；第三，SPSS主要用于分析截面数据，在时序和面板数据处理方面功能了了；最后，SPSS兼容菜单化和编程化操作，是名副其实的傻瓜软件。 STATA与EVIEWS都是我偏好的计量软件。前者完全编程化操作，后者兼容菜单化和编程化操作；虽然两款软件都能做简单的描述统计，但是较之 SPSS差了许多；STATA与EVIEWS都是计量软件，高级的计量分析能够在这两个软件里得到实现；STATA的扩展性较好，我们可以上网找自己需要的命令文件（.ado文件），不断扩展其应用，但EVIEWS 就只能等着软件升级了；另外，对于时序数据的处理，EVIEWS较强。 综上，各款软件有自己的强项和弱项，用什么软件取决于数据本身的属性及分析方法。EXCEL适用于处理小样本数据，SPSS、 STATA、EVIEWS可以处理较大的样本；EXCEL、SPSS适合做数据清洗、新变量计算等分析前准备性工作，而STATA、EVIEWS在这方面较差；制图制表用EXCEL；对截面数据进行统计分析用SPSS，简单的计量分析SPSS、STATA、EVIEWS可以实现，高级的计量分析用 STATA、EVIEWS，时序分析用EVIEWS。 关于因果性 做统计或计量，我认为最难也最头疼的就是进行因果性判断。假如你有A、B两个变量的数据，你怎么知道哪个变量是因（自变量），哪个变量是果（因变量）？ 早期，人们通过观察原因和结果之间的表面联系进行因果推论，比如恒常会合、时间顺序。但是，人们渐渐认识到多次的共同出现和共同缺失可能是因果关系，也可能是由共同的原因或其他因素造成的。从归纳法的角度来说，如果在有A的情形下出现B，没有A的情形下就没有B，那么A很可能是B的原因，但也可能是其他未能预料到的因素在起作用，所以，在进行因果判断时应对大量的事例进行比较，以便提高判断的可靠性。 有两种解决因果问题的方案：统计的解决方案和科学的解决方案。统计的解决方案主要指运用统计和计量回归的方法对微观数据进行分析，比较受干预样本与未接受干预样本在效果指标（因变量）上的差异。需要强调的是，利用截面数据进行统计分析，不论是进行均值比较、频数分析，还是方差分析、相关分析，其结果只是干预与影响效果之间因果关系成立的必要条件而非充分条件。类似的，利用截面数据进行计量回归，所能得到的最多也只是变量间的数量关系；计量模型中哪个变量为因变量哪个变量为自变量，完全出于分析者根据其他考虑进行的预设，与计量分析结果没有关系。总之，回归并不意味着因果关系的成立，因果关系的判定或推断必须依据经过实践检验的相关理论。虽然利用截面数据进行因果判断显得勉强，但如果研究者掌握了时间序列数据，因果判断仍有可为，其
手机微信QQ聊天记录取证方法(非常详细实用)
手机微信QQ聊天记录取证方法（非常详细实用） 如今，由于互联网为交易双方提供了跨越物理空间的沟通渠道，通过网络协商订立合同条款越来越成为追求交易便捷、降低成本的商事主体的选择。 在案件当中，通过微信、QQ、电子邮件协商确定双方权利义务的情况比比皆是，也成为认定案件关键事实的主要证据。目前互联网电子数据证据成为案件主要证据的比例逐步上升，甚至部分案件中此类证据，特别是微信证据成为当事人证明自己主张的唯一证据。 为了统一司法实践中互联网电子证据认定标准，南沙法院在全省率先出台《互联网电子数据证据举证、认证规程(试行)》(以下简称《规程》)。 《规程》对互联网电子数据证据的内涵予以了界定，依据及参考已经颁布施行的《电子签名法》以及尚在审议过程中的《电子商务法》，并结合法院审判实践中出现较多的证据类型，列举了短信、电子邮件、QQ、微信、支付宝或其他具备通讯、支付功能的互联网软件所产生的，能够有形地表现所载内容并可以随时调取查用的数据信息。 针对各种证据类型，《规程》对当事人向法院提供证据方面作出指引，包括固化证据的形式、使用的介质、展示证据的程序。同时法院也在立案窗口和
应诉送达时专门放置举证指引清单，对于提交此类证据的当事人及时进行指导，减少不规范的举证行为，提高审判效率。 《规程》还对法官采信电子证据的认证过程作出指引。对于通过公证、鉴证可以解决证据真实性认证问题的，引导当事人进行公证、鉴证，而对于没有进行公证、鉴证或者公证、鉴证内容尚不足以证实证据真实性的情况，主要通过电子数据证据中当事人的身份真实性、通讯内容的完整性来对证据进行认证。 ▌关于微信相关证据《规程》这样说 当事人提交微信相关证据需注意以下三方面： 1、使用终端设备登陆本方微信账户的过程演示。用于证明其持有微信聊天记录的合法性和本人身份的真实性。 2、聊天双方的个人信息界面。借助微信号不可更改的特点，并结合个人信息界面中显示的手机号码、头像等信息固定双方当事人的真实身份。 3、完整的聊天记录。根据微信聊天记录在使用终端中只能删除不能添加的特点，根据双方各自微信客户端完整聊天信息进行对比，以验证相关信息的完整性和真实性。 法官采信微信相关证据时如何做? 1、法官在采信微信相关证据时如何确定微信使用者身份? 微信并未强制实名认证，法官在采信微信相关证据时，根据当事人提供的对方微信号、绑定的手机号码以及聊天记录中透露的相关信息内容，法官可以
32款图片处理软件介绍
32款图片处理软件介绍（转） 色友们大概没有人不知道Photoshop大名的，要想得到好的照片后期处理是必不可少的。但是Photoshop也不是万能的，况且它的资源占用也非常的大，那么有没有其他的选择呢，答案是肯定的。下面我们就来向大家介绍32款小编常用的图像处理软件。 1.名称：ExifShow 查看数码照片EXIF信息 大小：303K 软件介绍：对DC发烧友来说，在查看一幅精美的数码照片时，肯定希望了解作者所使用的相机、曝光值、焦距值等参数，一般的做法是将这些数码照片下载回来，然后利用ACDSee 等软件查看EXIF信息，由于下载或保存的过程必不可少，因此操作稍稍麻烦了一些。安装了ExifShow插件，以后当我们在IE中浏览数码照片时，只要按一下鼠标右键，快捷菜单中就会出现“查看EXIF信息”的选项，马上就可以查看。在信息列表处单击鼠标右键，可以将选中的EXIF信息复制到剪贴板中或者另存为文本文件。假如有一些数码照片显示“该图片没有EXIF信息”，说明可能是经过了某种形式的处理而导致丢失了EXIF数据，或者是用不支持EXIF的数码相机拍摄的照片。 橡树下载：https://www.wendangku.net/doc/479491522.html,/download/software/1.rar 2.软件名称：ACDsee 7 简体中文化版 大小：24M 软件介绍：ACDSee 是目前最流行的数字图象处理软件，它能广泛应用于图片的获取、管理、浏览、优化甚至和他人的分享！使用ACDSee，你可以从数码相机和扫描仪高效获取图片，并进行便捷的查找、组织和预览。超过50 种常用多媒体格式被一网打尽！作为最重量级看图软件，它能快速、高质量显示您的图片，再配以内置的音频播放器，我们就可以享用它播放出来的精彩幻灯片了。Acdsee 还能处理如Mpeg 之类常用的视频文件。此外ACDSee 是您最得心应手的图片编辑工具，轻松处理数码影像，拥有的功能像去除红眼、剪切图像、锐化、浮雕特效、曝光调整、旋转、镜像等等，还能进行批量处理哦！ 橡树下载：https://www.wendangku.net/doc/479491522.html,/download/software/33.ra 3名称：True Photo 4.1 中文正式版
常用统计软件介绍
常用统计软件介绍
常用统计软件介绍 《概率论与数理统计》是一门实践性很强的课程。但是,目前在国内,大多侧重基本方法的介绍,而忽视了统计实验的教学。这样既不利于提高学生创新精神和实践能力,也使得这门课程的教学显得枯燥无味。为此,我们介绍一些常用的统计软件，以使学生对统计软件有初步的认识,为以后应用统计方法解决实际问题奠定初步的基础。 一、统计软件的种类 1.SAS 是目前国际上最为流行的一种大型统计分析系统，被誉为统计分析的标准软件。尽管价格不菲，SAS已被广泛应用于政府行政管理，科研，教育，生产和金融等不同领域，并且发挥着愈来愈重要的作用。目前SAS已在全球100多个国家和地区拥有29000多个客户群，直接用户超过300万人。在我国，国家信息中心，国家统计局，卫生部，中国科学院等都是SAS系统的大用户。尽管现在已经尽量“傻瓜化”，但是仍然需要一定的训练才可以使用。因此,该统计软件主要适合于统计工作者和科研工作者使用。 2.SPSS SPSS作为仅次于SAS的统计软件工具包，在社会科学领域有着广泛的应用。SPSS是世界上最早的统计分析软件，由美国斯坦福大学的三位研究生于20世纪60年代末研制。由于SPSS容易操作，输出漂亮，功能齐全，价格合理,所以很快地应用于自然科学、技术科学、社会科学的各个领域，世界上许多有影响的报刊杂志纷纷就SPSS 的自动统计绘图、数据的深入分析、使用方便、功能齐全等方面给予了高度的评价与称赞。迄今SPSS软件已有30余年的成长历史。全球
约有25万家产品用户，它们分布于通讯、医疗、银行、证券、保险、制造、商业、市场研究、科研教育等多个领域和行业，是世界上应用最广泛的专业统计软件。在国际学术界有条不成文的规定，即在国际学术交流中，凡是用SPSS软件完成的计算和统计分析，可以不必说明算法，由此可见其影响之大和信誉之高。因此,对于非统计工作者是很好的选择。 3.Excel 它严格说来并不是统计软件，但作为数据表格软件，必然有一定统计计算功能。而且凡是有Microsoft Office的计算机，基本上都装有Excel。但要注意，有时在装 Office时没有装数据分析的功能，那就必须装了才行。当然，画图功能是都具备的。对于简单分析，Excel 还算方便，但随着问题的深入，Excel就不那么“傻瓜”，需要使用函数，甚至根本没有相应的方法了。多数专门一些的统计推断问题还需要其他专门的统计软件来处理。 4.S-plus 这是统计学家喜爱的软件。不仅由于其功能齐全，而且由于其强大的编程功能，使得研究人员可以编制自己的程序来实现自己的理论和方法。它也在进行“傻瓜化”,以争取顾客。但仍然以编程方便为顾客所青睐。 5.Minitab 这个软件是很方便的功能强大而又齐全的软件，也已经“傻瓜化”，在我国用的不如SPSS与SAS那么普遍。
数据处理软件介绍.
Chapter4 Introduction to Analysis-of-Variance Procedures Chapter T able of Contents 52Chapter4.Introduction to Analysis-of-Variance Procedures SAS OnlineDoc?:Version8 Chapter4 Introduction to Analysis-of-Variance Procedures 54Chapter4.Introduction to Analysis-of-Variance Procedures The following section presents an overview of some of the fundamental features of analysis of variance.Subsequent sections describe how this analysis is performed with procedures in SAS/STAT software.For more detail,see the chapters for the individual procedures.Additional sources are described in the“References”section on page61. De?nitions Analysis of variance(ANOV Ais a technique for analyzing experimental data in which one or more response(or dependent or simply Yvariables are measured un-der various conditions identi?ed by one or more classi?cation variables.The com-binations of levels for the classi?cation variables form the cells of the experimental design for the data.For example,an experiment may measure weight change(the dependent variablefor men and women who participated in three different weight-loss programs.The six cells of the design are formed by the six combinations of sex (men,womenand program(A,B,C.
大数据可视化分析平台介绍
大数据可视化分析平台 一、背景与目标 基于邳州市电子政务建设的基础支撑环境，以基础信息资源库(人口库、法人库、宏观经济、地理库)为基础，建设融合业务展示系统，提供综合信息查询展示、信息简报呈现、数据分析、数据开放等资源服务应用。实现市府领导及相关委办的融合数据资源视角，实现数据信息资源融合服务与创新服务，通过系统达到及时了解本市发展的综合情况，及时掌握发展动态,为政策拟定提供依据。 充分运用云计算、大数据等信息技术，建设融合分析平台、展示平台，整合现有数据资源,结合政务大数据的分析能力与业务编排展示能力，以人口、法人、地理，人口与地理,法人与地理，实现基础展示与分析,融合公安、交通、工业、教育、旅游等重点行业的数据综合分析，为城市管理、产业升级、民生保障提供有效支撑。 二、政务大数据平台 1、数据采集和交换需求:通过对各个委办局的指定业务数据进行汇聚,将分散的数据进行物理集中和整合管理，为实现对数据的分析提供数据支撑。将为跨机构的各类业务系统之间的业务协同，提供统一和集中的数据交互共享服务。包括数据交换、共享和EＴL等功能。 ２、海量数据存储管理需求：大数据平台从各个委办局的业务系统里抽取的数据量巨大,数据类型繁杂,数据需要持久化的存储和访问。不论是结构化数据、半结构化数据，还是非结构化数据,经过数据存储引擎进行建模后，持久化保存在存储系统上。存储系统要具备
高可靠性、快速查询能力。 3、数据计算分析需求：包括海量数据的离线计算能力、高效即席数据查询需求和低时延的实时计算能力。随着数据量的不断增加，需要数据平台具备线性扩展能力和强大的分析能力,支撑不断增长的数据量，满足未来政务各类业务工作的发展需要，确保业务系统的不间断且有效地工作。 4、数据关联集中需求：对集中存储在数据管理平台的数据，通过正确的技术手段将这些离散的数据进行数据关联,即:通过分析数据间的业务关系，建立关键数据之间的关联关系，将离散的数据串联起来形成能表达更多含义信息集合，以形成基础库、业务库、知识库等数据集。 5、应用开发需求:依靠集中数据集,快速开发创新应用，支撑实际分析业务需要。 6、大数据分析挖掘需求:通过对海量的政务业务大数据进行分析与挖掘,辅助政务决策,提供资源配置分析优化等辅助决策功能， 促进民生的发展。
超好用的CAD图库资源,你需要的CAD图纸这里全都有!
超好用的CAD图库资源，你需要的CAD图纸这里全都有！ 现在网络上各种来源的CAD图纸资源良莠不齐，而且繁杂不好查找。我们在日常CAD工作中常常需要大量的cad图纸作为参考，这时候就需要一个好用又质量高的CAD资源图库了。小编给大家推荐迅捷CAD图库。 步骤一：首先，我们在浏览器里搜索“迅捷CAD图库”相关字样，找到迅捷CAD图库网址进入。如下图： 步骤二：进入到迅捷CAD官网，接着点击官网顶端的“每日一图”栏，切换到迅捷CAD图库“每日一图”。如下图：
步骤三：根据需要，在搜索栏里搜索需要的CAD图纸字样，或是直接点击对应的CAD图纸标签栏，就会跳转出需要查找的cad图纸的相关素材合集。如下图：
步骤四：从合集中选择我们需要的CAD图纸栏“工装家装CAD室内设计平面立面图块素材”，点击进入浏览详情页面。如下图：
步骤五：在查看浏览网页里，点击右上角的“立即下载”，就会跳转到百度云资源网盘下载界面。然后就可以下载需要的CAD 图纸资源压缩包素材.rar。如下图：
以上就是在迅捷CAD图库里查找下载需要的CAD图纸资源的具体步骤，真的特别实用，所有的CAD图纸全都是高质量的，而且完全免费提供给用户哦！
爱人者，人恒爱之；敬人者，人恒敬之；宽以济猛，猛以济宽，政是以和。将军额上能跑马，宰相肚里能撑船。 最高贵的复仇是宽容。有时宽容引起的道德震动比惩罚更强烈。 君子贤而能容罢，知而能容愚，博而能容浅，粹而能容杂。 宽容就是忘却，人人都有痛苦，都有伤疤，动辄去揭，便添新创，旧痕新伤难愈合，忘记昨日的是非，忘记别人先前对自己的指责和谩骂，时间是良好的止痛剂，学会忘却，生活才有阳光，才有欢乐。 不要轻易放弃感情，谁都会心疼；不要冲动下做决定，会后悔一生。也许只一句分手，就再也不见；也许只一次主动，就能挽回遗憾。
常用分子生物学软件简介
常用分子生物学软件 一、基因芯片： 1、基因芯片综合分析软件。 ArrayVision 一种功能强大的商业版基因芯片分析软件，不仅可以进行图像分析，还可以进行数据处理，方便protocol的管理功能强大，商业版正式版：6900美元。 Arraypro Media Cybernetics公司的产品，该公司的gelpro, imagepro一直以精确成为同类产品中的佼佼者，相信arraypro也不会差。 phoretix? Array Nonlinear Dynamics公司的基因片综合分析软件。 J-express 挪威Bergen大学编写，是一个用JAVA语言写的应用程序，界面清晰漂亮，用来分析微矩阵（microarray）实验获得的基因表达数据，需要下载安装JAVA运行环境后后，才能运行。 2、基因芯片阅读图像分析软件 ScanAlyze ，斯坦福的基因芯片基因芯片阅读软件，进行微矩阵荧光图像分析，包括半自动定义格栅与像素点分析。输出为分隔的文本格式，可很容易地转化为任何数据库。 3、基因芯片数据分析软件 Cluster 斯坦福的对大量微矩阵数据组进行各种簇（Cluster)分析与其它各种处理的软件。 SAM Significance Analysis of Microarrays 的缩写，微矩阵显著性分析软件，EXCEL软件的插件，由Stanford大学编制。 4．基因芯片聚类图形显示 TreeView 斯坦福开发的用来显示Cluster软件分析的图形化结果。现已和Cluster成为了基因芯片处理的标准软件。 FreeView 是基于JAVA语言的系统树生成软件，接收Cluster生成的数据，比Treeview增强了某些功能。 5．基因芯片引物设计 Array Designer DNA微矩阵（microarray）软件，批量设计DNA和寡核苷酸引物工具 二、RNA二级结构。 RNA Structure RNA Sturcture 根据最小自由能原理，将Zuker的根据RNA一级序列预测RNA二级结构的算法在软件上实现。预测所用的热力学数据是最近由Turner实验室获得。提供了一些模块以扩展Zuker算法的能力，使之为一个界面友好的RNA折叠程序。允许你同时打开多个数据处理窗口。主窗口的工具条提供一些基本功能：打开文件、导入文件、关闭文件、设置程序参数、重排窗口、以及即时帮助和退出程序。RNAdraw中一个非常非常重要的特征是鼠标右键菜单打开的菜单显示对鼠标当前所指向的对象/窗口可以使用的功能列表。RNA文库（RNA
各种处理图片软件的名称及作用
?软件名：光影魔术手 ?软件介绍：可以轻松地调节照片的白平衡、色彩等。 ?软件名：Noiseware ?软件介绍：可以方便地消除图片上的噪点。 ?软件名：PhotoZoom ?软件介绍：可以数倍放大照片，同时能较好地保证画质。 ?软件名：FaceFilter Studio ?软件介绍：给数码照片“补装”的软件。 ?软件名：FilmLoop ?软件介绍：可以把喜欢的画片以滚动的方式在屏幕上显示，并可添加说明文字或URL链接。 ?软件名：2D+3D Screensaver Maker ?软件介绍：把静态图片做成3D运动效果的屏保。 ?软件名：BetterJPEG ?软件介绍：编辑图片后，仅对编辑部分进行二次压缩，减少JPEG图片因多次编辑而造成的画质损失。 ?软件名：photoWORKS ?软件介绍：用于给图片批量添加相框。还可以简单地对图片进行处理。非常实用的一款免费工作。 ?软件名：recolored beta 060 ?软件介绍：利用非常简单的方法为照片上色，效果极佳。 ?软件名：UleadGIFAnimator505 ?软件介绍：一个“所见即所得”型的的GIF制作软件。 ?软件名：BatchImager ?软件介绍：真正的照片批量处理工具。 ?软件名：Blender ?软件介绍：免费强大的3D绘图工具。 ?软件名：FotoBatch ?软件介绍：功能比较丰富的图片编辑软件，最大特点是可以编辑脚本，对照片进行批处理。 ?软件名：TurboPhoto ?软件介绍：不仅可以方便地给数码照片加相框，更是数码照片后期处理的绝好帮手，操作简单，效果出色。 ?软件名：Wings 3D ?软件介绍：免费简洁的3D模型绘图工具。 ?软件名：Inkscape ?软件介绍：免费且开放源代码的矢量绘图工具。 ?软件名：Foto Mosaik
2020大数据分析的六大工具介绍
云计算大数据处理分析六大最好工具 一、概述 来自传感器、购买交易记录、网络日志等的大量数据，通常是万亿或EB的大小，如此庞大的数据，寻找一个合适处理工具非常必要，今天我们为大家分享在大数据处理分析过程中六大最好用的工具。 我们的数据来自各个方面，在面对庞大而复杂的大数据，选择一个合适的处理工具显得很有必要，工欲善其事，必须利其器，一个好的工具不仅可以使我们的工作事半功倍，也可以让我们在竞争日益激烈的云计算时代，挖掘大数据价值，及时调整战略方向。 大数据是一个含义广泛的术语，是指数据集，如此庞大而复杂的，他们需要专门设计的硬件和软件工具进行处理。该数据集通常是万亿或EB的大小。这些数据集收集自各种各样的来源：传感器、气候信息、公开的信息、如杂志、报纸、文章。大数据产生的其他例子包括购买交易记录、网络日志、病历、事监控、视频和图像档案、及大型电子商务。大数据分析是在研究大量的数据的过程中寻找模式，相关性和其他有用的信息，可以帮助企业更好地适应变化，并做出更明智的决策。 二、第一种工具：Hadoop Hadoop 是一个能够对大量数据进行分布式处理的软件框架。但是 Hadoop 是以一种可靠、高效、可伸缩的方式进行处理的。Hadoop 是可靠的，因为它假设计算元素和存储会失败，因此它维护多个工作数据副本，确保能够针对失败的节点重新分布处理。Hadoop 是高效的，因为它以并行的方式工作，通过并行处理加快处理速度。Hadoop 还是可伸缩的，能够处理 PB 级数据。此外，Hadoop 依赖于社区服务器，因此它的成本比较低，任何人都可以使用。 Hadoop是一个能够让用户轻松架构和使用的分布式计算平台。用户可以轻松地在Hadoop上开发和运行处理海量数据的应用程序。它主要有以下几个优点： ●高可靠性。Hadoop按位存储和处理数据的能力值得人们信赖。 ●高扩展性。Hadoop是在可用的计算机集簇间分配数据并完成计算任务的，这些集簇可以方便地扩 展到数以千计的节点中。 ●高效性。Hadoop能够在节点之间动态地移动数据，并保证各个节点的动态平衡，因此处理速度非 常快。 ●高容错性。Hadoop能够自动保存数据的多个副本，并且能够自动将失败的任务重新分配。 ●Hadoop带有用 Java 语言编写的框架，因此运行在 Linux 生产平台上是非常理想的。Hadoop 上的 应用程序也可以使用其他语言编写，比如 C++。 三、第二种工具：HPCC HPCC，High Performance Computing and Communications(高性能计算与通信)的缩写。1993年，由美国科学、工程、技术联邦协调理事会向国会提交了“重大挑战项目：高性能计算与通信”的报告，
16种常用的大数据分析报告方法汇总情况
一、描述统计 描述性统计是指运用制表和分类，图形以及计筠概括性数据来描述数据的集中趋势、离散趋势、偏度、峰度。 1、缺失值填充：常用方法：剔除法、均值法、最小邻居法、比率回归法、决策树法。 2、正态性检验：很多统计方法都要求数值服从或近似服从正态分布，所以之前需要进行正态性检验。常用方法：非参数检验的K-量检验、P-P图、Q-Q图、W检验、动差法。 二、假设检验 1、参数检验 参数检验是在已知总体分布的条件下（一股要求总体服从正态分布）对一些主要的参数(如均值、百分数、方差、相关系数等）进行的检验。 1）U验使用条件：当样本含量n较大时，样本值符合正态分布 2）T检验使用条件：当样本含量n较小时，样本值符合正态分布 A 单样本t检验：推断该样本来自的总体均数μ与已知的某一总体均数μ0 (常为理论值或标准值)有无差别； B 配对样本t检验：当总体均数未知时，且两个样本可以配对，同对中的两者在可能会影响处理效果的各种条件方面扱为相似； C 两独立样本t检验：无法找到在各方面极为相似的两样本作配对比较时使用。 2、非参数检验 非参数检验则不考虑总体分布是否已知，常常也不是针对总体参数，而是针对总体的某些一股性假设（如总体分布的位罝是否相同，总体分布是否正态）进行检验。 适用情况：顺序类型的数据资料，这类数据的分布形态一般是未知的。 A 虽然是连续数据，但总体分布形态未知或者非正态； B 体分布虽然正态，数据也是连续类型，但样本容量极小，如10以下； 主要方法包括：卡方检验、秩和检验、二项检验、游程检验、K-量检验等。 三、信度分析 检査测量的可信度，例如调查问卷的真实性。
简单高效照片处理软件集合
简单高效照片处理软件集合 来源：直线新闻网 | 时间：2014-04-24 11:37:05 | 查看评论[0] | 我顶[0] 五一假期即将来临，出游拍照成为必不可少的事，然而拍摄回来堆积如山的照片往往令人束手无策。虽说现在的照片处理软件早已不比从前，无论便利性还是处理效果上，都要比以往更适合普通用户。但……还是那句话，软件用时方恨少，对于大多数使用者来说，他们也许并不清楚看图时是美图看看更方便还是Picasa更好一点。总之这的确是一个令人挠头的问题，因为……这可能就是你的照片为何一直无法搞定的最根本原因。 1. Acropano ——最简单的全景图制作工具 全景图是近年来的一个新宠，许多新款手机、相机都已内置了这项功能。但……如果你的相机不支持怎么办？很简单，下载一款Acropano手工合成全景图吧。整个操作非常简单，将拍好的照片加入软件（拍摄时最好保持照片与照片间的一定重叠，以便软件进行辨识），再依真实场景对照片排序，接下来拼接自动开始，最终你需要做的只要拖动红框确定最终要保留的照片范围即可。好不好！咱们直接拿图说话！ 最关键的是把照片排好顺序
确定需要保留的部分 好不好？直接拿图说话！ 2. Snap2IMG ——为照片建目录 海量的照片放在电脑，查找起来终归是件麻烦事。这款小软件的功能非常直接，就是为硬盘里的照片（位置可指定）做一个目录。当然这个目录并不是单纯的文字描述，而是最容易被人分辨的缩略图。同时里面会标明了不同照片的具体位置，总之……按图索骥的设计，很适合照相海量的同学一试。
为照片生成快照“目录” 这是最终“目录”的一个缩影，相信可以说明一切了！
2019大数据分析软件介绍
大数据分析是什么？大数据分析软件有哪些？这是现在这个信息时代每一个企业管理者、经 营参与者都需要了解的。今天，小编就来针对性地总结一下，什么是大数据分析，以及2019 年主流的商业大数据分析软件。 一、大数据分析是什么 从各种各样类型的数据中，快速获得有价值信息的能力，就是大数据技术。 大数据最核心的价值就是在于对于海量数据进行存储和分析。物联网、云计算、移动互联网、车联网、手机、平板电脑、PC以及遍布地球各个角落的各种各样的传感器……我们每天能接触到数据海洋。 大数据分析的特点有以下几点：第一，数据体量巨大。从TB级别，跃升到PB级别。第二，数据类型繁多，包括网络日志、视频、图片、地理位置信息等等。第三，价值密度低。以视 频为例，连续不间断监控过程中，可能有用的数据仅仅有一两秒。第四，处理速度快。最后 这一点也是和传统的数据挖掘技术有着本质的不同。 大数据分析软件让企业能够从数据仓库获得洞察力，从而在数据驱动的业务环境中提供重要 的竞争优势。 二、 2019年大数据分析软件 1.Apache Hadoop Hadoop 是一个能够对大量数据进行分布式处理的软件框架。能够处理 PB 级数据。此外，Hadoop 依赖于社区服务器，因此它的成本比较低，任何人都可以使用。它处理速度非常快，并能够自动保存数据的多个副本。另外，带有用 Java 语言编写的框架，因此运行在 Linux 生 产平台上是非常理想的。Hadoop 上的应用程序也可以使用其他语言编写，比如 C++。 2.Storm Storm是自由的开源软件，一个分布式的、容错的实时计算系统。Storm可以非常可靠的处理 庞大的数据流，用于处理Hadoop的批量数据。 Storm很简单，支持许多种编程语言，使用 起来非常有趣。Storm由Twitter开源而来，其它知名的应用企业包括Groupon、淘宝、支付宝、阿里巴巴、乐元素、Admaster等等。应用于许多领域：实时分析、在线机器学习、不停 顿的计算、分布式RPC、 ETL等。 3.Pentaho BI
图片库系统平台方案
图片库系统平台方案 一、图片库系统平台定位 一个图片增值服务的业务平台、一个摄影师/记者/读者的预约沟通平台。 二、图片管理系统意义 随着互联网信息规模的增大，图片内容越来越丰富，互联网已经迈入“读图时代”。 因此图片需要具有特定的组织和管理方式、支持组图、分类、关联、属性检索等一系列图片特殊管理功能。重视图片的版权和传播途径。在图片的海洋中突出图片本质特征和真正的价值，集成多种方式进行共享和沟通 三、图片管理系统概述 （一）图片系统应用场景 1、通讯社、媒体报社、杂志社的自有版权图片的管理、共享和服务； 2、媒体报社、政府、企业、事业单位接收和购买的图片资源的整理、分类、内部服务和再利用； 3、单位间图片资源互换； 4、委托代为售卖的图片，建设图片中介服务； 5、图片友好交流活动平台； 6、网民根据系统模板自由开设个展。
（二）系统概述： 集外部采集、内部编发、信息服务、交流互动、图片电子商务于一体的图片系统. 图片管理系统：面向用户群体：外网和内网，1000人以上； 功能：功能复杂，以后期制作、互动、营销为主，建设特色的图片平台； （三）详细功能介绍： 1、批量上载、下载、图片个人管理； 2、断点续传，适合移动办公、远程上传，等各种网络条件情况； 3、批量图片采集：定制数据转换工具，将现有图片资源整理成图片网系统所能接收的格式，然后通过底层数据交换方式批量导入；
（图片发布系统工作模式简图） 4、图片自动加工：各种图片格式转换成JPG ；提取数码相机光圈、感光度、拍摄速度、拍摄时间、相机品牌型号等信息；自动压缩，生成缩略图；加载水印；有效提高上传、浏览速度。 5、图片编辑和管理：属性和分类标注，支持组图和多级分类；组稿，生成图片专题和图片故事；图片分级，进行存储管理；图片撤稿；流程管理；留资图片管理 6、图片发布：在线签发；多栏目签发；自动定时增量发布；最新图片、一周图片等多种浏览方式 7、用户和权限管理 （1）注册审批：填写用户名、密码、真实姓名、联系电话、E-mail 等信息；采用单向加密算法对密码进行加密处理； 系统管
常用数据分析方法分类介绍(注明来源)
常用数据分析方法有那些 文章来源：ECP数据分析时间：2013/6/2813:35:06发布者：常用数据分析（关注：554） 标签： 本文包括： 常用数据分析方法：聚类分析、因子分析、相关分析、对应分析、回归分析、方差分析； 问卷调查常用数据分析方法：描述性统计分析、探索性因素分析、Cronbach’a 信度系数分析、结构方程模型分析(structural equations modeling)。 数据分析常用的图表方法：柏拉图(排列图)、直方图(Histogram)、散点图(scatter diagram)、鱼骨图（Ishikawa）、FMEA、点图、柱状图、雷达图、趋势图。 数据分析统计工具：SPSS、minitab、JMP。 常用数据分析方法: 1、聚类分析（Cluster Analysis） 聚类分析指将物理或抽象对象的集合分组成为由类似的对象组成的多个类的分析过程。聚类是将数据分类到不同的类或者簇这样的一个过程，所以同一个簇中的对象有很大的相似性，而不同簇间的对象有很大的相异性。聚类分析是一种探索性的分析，在分类的过程中，人们不必事先给出一个分类的标准，聚类分析能够从样本数据出发，自动进行分类。聚类分析所使用方法的不同，常常会得到不同的结论。不同研究者对于同一组数据进行聚类分析，所得到的聚类数未必一致。 2、因子分析（Factor Analysis） 因子分析是指研究从变量群中提取共性因子的统计技术。因子分析就是从大量的数据中寻找内在的联系，减少决策的困难。 因子分析的方法约有10多种，如重心法、影像分析法，最大似然解、最小平方法、阿尔发抽因法、拉奥典型抽因法等等。这些方法本质上大都属近似方法，是以相关系数矩阵为基础的，所不同的是相关系数矩阵对角线上的值，采用不同的共同性□2估值。在社会学研究中，因子分析常采用以主成分分析为基础的反覆法。 3、相关分析（Correlation Analysis） 相关分析（correlation analysis），相关分析是研究现象之间是否存在某种依存关系，并对具体有依存关系的现象探讨其相关方向以及相关程度。相关关系是一种非确定性的关系，例如，以X和Y分别记一个人的身高和体重，或分别记每公顷施肥量与每公顷小麦产量，则X与Y显然有关系，而又没有确切到可由其中的一个去精确地决定另一个的程度，这就是相关关系。 4、对应分析（Correspondence Analysis） 对应分析(Correspondence analysis)也称关联分析、R-Q型因子分析，通过分析由定性变量构成的交互汇总表来揭示变量间的联系。可以揭示同一变量的各个类别之间的差异，以及不同变量各个类别之间的对应关系。对应分析的基本思想是将一个联列表的行和列中各元素的比例结构以点的形式在较低维的空间中表示出来。
常用统计软件介绍
常用统计软件介绍 《概率论与数理统计》是一门实践性很强的课程。但是,目前在国内,大多侧重基本方法的介绍,而忽视了统计实验的教学。这样既不利于提高学生创新精神和实践能力,也使得这门课程的教学显得枯燥无味。为此,我们介绍一些常用的统计软件，以使学生对统计软件有初步的认识,为以后应用统计方法解决实际问题奠定初步的基础。 一、统计软件的种类 1.SAS 是目前国际上最为流行的一种大型统计分析系统，被誉为统计分析的标准软件。尽管价格不菲，SAS已被广泛应用于政府行政管理，科研，教育，生产和金融等不同领域，并且发挥着愈来愈重要的作用。目前SAS已在全球100多个国家和地区拥有29000多个客户群，直接用户超过300万人。在我国，国家信息中心，国家统计局，卫生部，中国科学院等都是SAS系统的大用户。尽管现在已经尽量“傻瓜化”，但是仍然需要一定的训练才可以使用。因此,该统计软件主要适合于统计工作者和科研工作者使用。 2.SPSS SPSS作为仅次于SAS的统计软件工具包，在社会科学领域有着广泛的应用。SPSS是世界上最早的统计分析软件，由美国斯坦福大学的三位研究生于20世纪60年代末研制。由于SPSS容易操作，输出漂亮，功能齐全，价格合理,所以很快地应用于自然科学、技术科学、社会科学的各个领域，世界上许多有影响的报刊杂志纷纷就SPSS 的自动统计绘图、数据的深入分析、使用方便、功能齐全等方面给予了高度的评价与称赞。迄今SPSS软件已有30余年的成长历史。全球
约有25万家产品用户，它们分布于通讯、医疗、银行、证券、保险、制造、商业、市场研究、科研教育等多个领域和行业，是世界上应用最广泛的专业统计软件。在国际学术界有条不成文的规定，即在国际学术交流中，凡是用SPSS软件完成的计算和统计分析，可以不必说明算法，由此可见其影响之大和信誉之高。因此,对于非统计工作者是很好的选择。 3.Excel 它严格说来并不是统计软件，但作为数据表格软件，必然有一定统计计算功能。而且凡是有Microsoft Office的计算机，基本上都装有Excel。但要注意，有时在装 Office时没有装数据分析的功能，那就必须装了才行。当然，画图功能是都具备的。对于简单分析，Excel 还算方便，但随着问题的深入，Excel就不那么“傻瓜”，需要使用函数，甚至根本没有相应的方法了。多数专门一些的统计推断问题还需要其他专门的统计软件来处理。 4.S-plus 这是统计学家喜爱的软件。不仅由于其功能齐全，而且由于其强大的编程功能，使得研究人员可以编制自己的程序来实现自己的理论和方法。它也在进行“傻瓜化”,以争取顾客。但仍然以编程方便为顾客所青睐。 5.Minitab 这个软件是很方便的功能强大而又齐全的软件，也已经“傻瓜化”，在我国用的不如SPSS与SAS那么普遍。