Last modified: 2005 Jun 30

Probability Distribution Functions and Random Number Generators

• Risk Management Library (including copulas)

  Author: Thierry Roncalli
  Date: various
  Abstract: The library and the programs used to illustrate the "La gestion des Risques Financiers".  250 Programs : Basel II and Cooke Ratio (Market risk / Credit Risk / Operational Risk) Multiple risks management (Copula functions /  Multiple risks agregation) Credit risk management (Credit derivatives / PD / LGD / Default Correlations / CPM / RAROC)
  Archived 20050630: library (zipped)
  

  Note: see also http://gro.creditlyonnais.fr/content/rd/home_copulas.htm
• DISTRIB (Library for Statistical Distributions)

  Author: Schlittgen
  Date: 200111..
  Abstract: Library for Statistical Distributions
  

  Note: see documentation.
• Stable random number generator subroutine rndKMsta for GAUSS 3.6+ is based on the GAUSS 3.6+ "Kiss Monster" rndKMu random number generator. (McCulloch May01)
• Extreme Value Theory and Estimation (Roncalli Feb01)
• Uunstandardized, truncated normal distributions & random numbers (King 97)
  (check for update)
• Laplace-Distributed Random Numbers using the inverse-cdf technique (Loretan Aug99)
• General PDFs

  Author: David Baird
  Date: 199908..
  Abstract: Probability Distributions and related functions: Normal, Students T, Chi square, F, Poisson, Binomial, Negative Binomial, Gamma, Beta amd Multinomial.
  

• Cauchy generator

  Author: David Baird
  Date: 19960712
  Abstract: Create normalized cauchy distributed random variables
  

• Derivatives of Loggamma

  Author: Paul Fackler
  Date: 199805..
  Abstract: Calculates the first four derivatives of the loggamma function.
  

• integrate the multivariate normal density

  Author: Geert Molenberghs
  Date: 199004..
  Abstract: GAUSS-version of the algorithm by M. Shervish
  

• complementary error function

  Author: Allen Wilkinson
  Date: 199508..
  Abstract: lower 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