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

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

2010-03-25

arxiv.org/abs/1003.4890v1

Computational Statistics \& Data Analysis / Computational Statistics and Data Analysis 54, 3 (2010) 724-731

Statistics

Methodology

Scientific paper

10.1016/j.csda.2008.11.004

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.

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