Exact Distribution of the Ratio of Gamma and Rayleigh Random Variables

M. Shakil, B. M. Golam Kibria

Abstract


The distributions of the ratio of two independent random variables arise in many applied problems and have been extensively studied by many researchers. This article derives the distributions of the ratio Z=|x/y| , when x and y are gamma and Rayleigh random variables respectively and are distributed independently of each other. The associated pdf, cdf, and moments have been given in terms of different special functions, for examples, confluent hypergeometric function, parabolic-cylinder function and beta functions. Some plots for the cdf and pdf associated with the distribution of the ratio have been provided.

Full Text:

PDF


DOI: http://dx.doi.org/10.18187/pjsor.v2i2.91

Refbacks

  • There are currently no refbacks.




Copyright (c)

Title

Exact Distribution of the Ratio of Gamma and Rayleigh Random Variables

Keywords

-

Description

The distributions of the ratio of two independent random variables arise in many applied problems and have been extensively studied by many researchers. This article derives the distributions of the ratio Z=|x/y| , when x and y are gamma and Rayleigh random variables respectively and are distributed independently of each other. The associated pdf, cdf, and moments have been given in terms of different special functions, for examples, confluent hypergeometric function, parabolic-cylinder function and beta functions. Some plots for the cdf and pdf associated with the distribution of the ratio have been provided.

Date

2006-07-01

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol 2. No. 2, July 2006



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810