Implementing Bayesian predictive procedures: The K-prime and K-square distributions

Authors:
Jacques Poitevineau;Bruno Lecoutre
Affiliations:
ERIS and UMR 7190, IJLRA/LAM/LCPE, C.N.R.S., Université Pierre et Marie Curie, 11 rue de Lourmel, 75015 Paris, France;ERIS and UPRESA 6085, Laboratoire de Mathématiques Raphaël Salem, C.N.R.S. et Université de Rouen, Mathématiques, Site Colbert, 76821 Mont-Saint-Aignan Cedex, France
Venue:
Computational Statistics & Data Analysis
Year:
2010

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Abstract

The implementation of Bayesian predictive procedures under standard normal models is considered. Two distributions are of particular interest, the K-prime and K-square distributions. They also give exact inferences for simple and multiple correlation coefficients. Their cumulative distribution functions can be expressed in terms of infinite series of multiples of incomplete beta function ratios, thus adequate for recursive calculations. Efficient algorithms are provided. To deal with special cases where possible underflows may prevent a recurrence to work properly, a simple solution is proposed which results in a procedure which is intermediate between two classes of algorithm. Some examples of applications are given.