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

Jacques Poitevineau (1) , Bruno Lecoutre (2)

1 DALEMBERT - Institut Jean Le Rond d'Alembert
2 LMRS - Laboratoire de Mathématiques Raphaël Salem

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.

Domaines: Méthodologie [stat.ME]

Jacques Poitevineau, Bruno Lecoutre. Implementing Bayesian predictive procedures: The K-prime and K-square distributions. Computational Statistics and Data Analysis, 2010, 54 (3), pp.724-731. ⟨10.1016/j.csda.2008.11.004⟩. ⟨hal-00462556⟩