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

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  • Poitevineau, Jacques
  • Lecoutre, Bruno

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.

Suggested Citation

  • Poitevineau, Jacques & Lecoutre, Bruno, 2010. "Implementing Bayesian predictive procedures: The K-prime and K-square distributions," Computational Statistics & Data Analysis, Elsevier, vol. 54(3), pages 724-731, March.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:3:p:724-731
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    1. Benton, Denise & Krishnamoorthy, K., 2003. "Computing discrete mixtures of continuous distributions: noncentral chisquare, noncentral t and the distribution of the square of the sample multiple correlation coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 43(2), pages 249-267, June.
    2. Inoue, Lurdes Y.T. & Berry, Donald A. & Parmigiani, Giovanni, 2005. "Relationship Between Bayesian and Frequentist Sample Size Determination," The American Statistician, American Statistical Association, vol. 59, pages 79-87, February.
    3. Bruno Lecoutre & Jean‐Luc Guigues & Jacques Poitevineau, 1992. "Distribution of Quadratic Forms of Multivariate Generalized Student Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(3), pages 617-627, November.
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    5. David J. Spiegelhalter & Laurence S. Freedman & Mahesh K. B. Parmar, 1994. "Bayesian Approaches to Randomized Trials," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 157(3), pages 357-387, May.
    6. Lecoutre, Marie-Paule & Rouanet, Henry, 1993. "Predictive Judgments in Situations of Statistical Analysis," Organizational Behavior and Human Decision Processes, Elsevier, vol. 54(1), pages 45-56, February.
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    Cited by:

    1. Steven E. Pav, 2015. "Inference on the Sharpe ratio via the upsilon distribution," Papers 1505.00829, arXiv.org, revised Aug 2021.

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