Probability Distribution Functions and Random Number Generators

• General PDFs (Baird Aug 99)
• Derivatives of Loggamma (Fackler, May98) Calculates the first four derivatives of the loggamma function.
• GAUSS-version of the algorithm by M. Shervish to integrate the multivariate normal density. (Molenberghs, Apr90)
• A better complementary error function (Wilkinson Aug95) with fractional error everywhere less than 1.2e-7 "based on Chebyshev fitting to an inspired guess as to the functional form".
• Bivariate Normal (van der Ende, Jun96 ) calculates cdfbvn with increased accuracy (with more approximating coeffcients).
• Symmetric Stable PDF (McCulloch 95)
• Gamma Distributed Random Numbers by Ronald Schoenberg (Jul95) is a transcription of a Fortran program, appearing in Principles of Random Variate Generation by John Dagpunar, for generating gamma distributed random variables.
• Gamma-Distributed Random Numbers (Mittelhammer Dec92; Heckelei Jun93) generaties gamma-distributed random numbers using various methods depending on the value of the alpha parameter.
• ANURAG.SRC by Anurag Banerjee (Apr97) inludes two procedures: IMHOF1(A,B,x) computes the distribution function P(u'Au/u'Bu < x) where u dist as N(0,I) and A sym matrix and B is a psd matrix; IMHOFINV(A,B,X1,PROB) computes the inverse.
• Stable Random Number Generators (McCulloch, Aug96).
• Inverse Normal Distribution (Suzuki, May95)
• Inverse CDFN (Mackin Nov96; Inkmann Nov96) computes the inverse function of CDFN using the approximation method based on Abramowitz and Stegun (1970).
• Loggamma Function And Its Derivatives (Fackler, Aug95)
• Integrate Multivariate Normal (Molenberghs Sep96) implements the Shervish algorithm to integrate the multivariate normal density.
• Risk Neutral Density Estimation Cameroon Rookley