Four Applications of a Bivariate Pareto Distribution

✍ Scribed by T. P. Hutchinson

• Publisher: John Wiley and Sons
• Year: 1979
• Tongue: English
• Weight: 634 KB
• Volume: 21
• Category: Article
• ISSN: 0323-3847
• DOI: 10.1002/bimj.4710210605

✦ Synopsis

The following model, of "latent structure'' type, is considered: in each subpopulation, X and Y are random variables drawn independently from the same exponential distribution, and the parameter of the exponential distribution varies between subpopulations with a Gamma density. Over the whole population, X and Y are then positively correlated, and jointly have a bivariate PABETO distribution. Four examples show how this distribution ia useful in analysing ordered contingency tables in which the two dimemions can be regarded as alternative measures of the same thing: the injuries to the two drivers in a road accident, or the severity of a lesion present in a patient as assessed by two physicians, for instance.

Two extensions are considered: (a) allowing X and Y to have Gamma distributions, with each subpopulation having the same shape parameter but different scale parameters; (b) allowing the scale parameter for Y to be correlated with the scale parameter for X, rather than being identical to it. A new bivariste distribution with three shape parameters is derived, expressed in terms of a genewlised hypergeometric function.