A generalized gamma model associated with a Bessel function

Abstract

A new probability density function associated with a Bessel function is introduced, which is the generalization of a gamma-type distribution. Some of its special cases are also mentioned. Multivariate analogue, conditional density, best predictor function, Bayesian analysis, etc., connected with this new density are also introduced. Suitability of this density as a good model in Bayesian inference and regression theory is also discussed.

Keywords:

• multivariate gamma density
• Bessel function
• Bayesian analysis
• regression analysis

AMS 1991 Subject Classifications :

• 33B15
• 33C10
• 62F15
• 62J05

Acknowledgements

The author would like to thank the Department of Science and Technology, Government of India, New Delhi, for the financial assistance for this work under project number SR/S4/MS: 287/05 and the Centre for Mathematical Sciences for providing all facilities. The author would also like to thank Prof. A. M. Mathai for the fruitful discussion of the article. This paper was presented at the international conference on “Analytical Methods of Analysis and Differential Equations AMADE-09” held at Minsk, Belarus from 14-19 September 2009.\\