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).