CharFunTool

The MATLAB Characteristic Functions Toolbox (CharFunTool) consists of a set of algorithms for evaluating selected characteristic functions and algorithms for numerical inversion of the combined and/or compound characteristic functions, used to evaluate the cumulative distribution function (CDF), the probability density function (PDF), and/or the quantile function (QF).

Release History:

v1.5.1
CHARACTERISTICS FUNCTIONS of null-distributions of the following test statistics based on the likelihood ratio:

• cfTest_Bartlett,
• cfTest_CompoundSymmetry,
• cfTest_EqualityCovariances,
• cfTest_EqualityMeans,
• cfTest_EqualityPopulations,
• cfTest_Independence,
• cfTest_Sphericity.

v1.5.0
NEW/REDEFINED INVERSION ALGORITHM FUNCTIONS:

• cf2Dist,
• cf2DistGP,
• cf2DistGPA,
• cf2DistGPT,
• cf2CDF,
• cf2PDF,
• cf2QF.

NEW UTILITY FUNCTIONS: AcceleratedSum, IntegralGK.

CharFunTool ver1.5.0 introduces new function cf2Dist (inversion algorithm) and redefines the function cf2DistGP.

cf2DistGP is an alias name for the algorithm cf2DistGPT, the inversion formula based on the simple trapezoidal rule (denoted as cfDistGP in the previous versions of CharFunTool).

cf2Dist is an alias name for the inversion algorithm specified by ALGORITHM name (string): [result,cdf,pdf,qf] = cf2Dist(cf,x,prob,options,algorithm). If empty, default value is algorithm = 'cf2DistGPA'.

The inversion algorithm cf2DistGPT is the original algorithm The inversion formula cf2DistGPA calculates the CDF/PDF/QF from the characteristic function CF by using the Gil-Pelaez inversion formulae. In fact, cf2DistGPA uses the the adaptive Gauss-Kronod quadrature rule for numerical integration of the oscillatory integrand function, which is divided into sub-intervals (found by a fast root-finding algorithm FindRoots) and subsequent application of the convergence acceleration techniques for computing the limit of the resulted alternating series, implemented in the algorithm AcceleratedSum. For more details see, e.g., Cohen et al. (2000) and Sidi (2011).

CharFunTool

CharFunTool

The MATLAB Characteristic Functions Toolbox (CharFunTool) consists of a set of algorithms for evaluating selected characteristic functions and algorithms for numerical inversion of the combined and/or compound characteristic functions, used to evaluate the cumulative distribution function (CDF), the probability density function (PDF), and/or the quantile function (QF).

Release History:

v1.4.2
NEW FUNCTIONS:

• cfX_Bartlett,
• SqrtZX.

v1.4.1
In release v1.4.1 are introduced the function LISTs for all categories of functions:

• !Applications_LIST.txt,
• !CF_InvAlgorithms_LIST,
• !CF_Repository_LIST,
• !CF_Tools_LIST,
• !CF_Utilities_LIST,
• !Data_LIST,
• !Examples_LIST.

NEW FUNCTIONS:

• RenewalProcessPMF (PMF of the renewal process defined by the holding time distribution specified by its CF),

Added new interpolant functions:

• PDFinterp,
• CDFinterp,
• QFinterp,
• RNDinterp.

Auxiliary transformation functions:

• LogPDF2PDF,
• LogCDF2CDF

and the unwrapped-version of sqrt (SqrtZX).

v1.4.0
In release v1.4.0 are introduced new characteristic functions related to the CHI distribution, the NON-CENTRAL CHI distribution and the distributions of the LOG-TRANSFORMED random variables, which allows to evaluate distribution of linear combinations of the random variables and the log-transformed random variables:

• cf_Chi,
• cf_ChiNC,
• cf_MaxwellBoltzmann,
• cf_MaxwellBoltzmannNC,
• cf_Nakagami,
• cf_NakagamiNC,
• cf_Rayleigh,
• cf_RayleighNC,
• cf_Rice,
• cf_LogRV_Chi,
• cf_LogRV_ChiNC,
• cf_LogRV_MaxwellBoltzmann,
• cf_LogRV_MaxwellBoltzmannNC,
• cf_LogRV_Nakagami,
• cf_LogRV_NakagamiNC,
• cf_LogRV_Rayleigh,
• cf_LogRV_RayleighNC,
• cf_LogRV_Rice, and also
• cf_LogRV_Weibull.

CharFunTool

The MATLAB Characteristic Functions Toolbox (CharFunTool) consists of a set of algorithms for evaluating selected characteristic functions and algorithms for numerical inversion of the combined and/or compound characteristic functions, used to evaluate the cumulative distribution function (CDF), the probability density function (PDF), and/or the quantile function (QF).

Release History:

v1.3.0
New and/or updated utility functions: cf_GeneralizedExponential. This release is suggested as source version for creating the R package CharFunToolR.

CharFunTool

The MATLAB Characteristic Functions Toolbox (CharFunTool) consists of a set of algorithms for evaluating selected characteristic functions and algorithms for numerical inversion of the combined and/or compound characteristic functions, used to evaluate the cumulative distribution function (CDF), the probability density function (PDF), and/or the quantile function (QF).

Release History:

v1.2.1
New and/or updated utility functions:

• GammaMulti
• GammaMultiLog,
• Hypergeom2F1,
• Hypergeom1F1MatApprox.

New characteristic functions:

• cf_Laplace,
• cfS_Laplace,
• cf_Gumbel.

Update of some cf_logRVs, e.g. cf_LogRV_GammaNC.

v1.2.0
The MATLAB GUI application CRMTool was included as an integral part of CharFunTool Applications Section, see CharFunTool\Applications\APPL_RiskModeling\CRMTool.
CRMTool (The Collective Risk Model Tool) is an Aggregate Loss Distribution Calculator, suggested to evaluate the Collective Risk Model (CRM) compound Aggregate Loss Distribution (ALD) and the associated quantiles, denoted also as the Value at Risk (VaR).

CharFunTool

The MATLAB Characteristic Functions Toolbox (CharFunTool) consists of a set of algorithms for evaluating selected characteristic functions and algorithms for numerical inversion of the combined and/or compound characteristic functions, used to evaluate the cumulative distribution function (CDF), the probability density function (PDF), and/or the quantile function (QF).

Release History:

v1.1.5
Updated the utility function Hypergeometric1F1, the confluent hypergeometric function 1F1(a;b;z) also known as the Kummer's function M(a,b,z).

v1.1.4
CharFunTool v1.1.4 includes new Applications folder with APPL_MultivariateAnalysis (applications for Multivariate Statistical Analysis). This version includes algorithms for computing p-values of selected LRT statistics (for testing independence, equality of means, equality of covariances, equality of normal populations, and sphericity) and their null distribution (CF/PDF/CDF/QF).

v1.1.3
CharFunTool v1.1.3 includes algorithm for computing the hypergeometric function of a matrix argument (the truncated sum of its series expansion) , used for evaluation CF of the non-central Wilks distribution, cf_LogRV_WilksLambdaNC.

v1.1
CharFunTool v1.1 includes new inversion algorithm cf2DistBV, based on using the Gil-Pelaez inversion formulae and the BAKHVALOV-VASILEVA quadrature method for computing the Fourier integrals.

CharFunTool

The MATLAB Characteristic Functions Toolbox (CharFunTool) consists of a set of algorithms for evaluating selected characteristic functions and algorithms for numerical inversion of the combined and/or compound characteristic functions, used to evaluate the cumulative distribution function (CDF), the probability density function (PDF), and/or the quantile function (QF).