The bivariate noncentral chi-square distribution – a compound distribution approach

Yunus, Rossita M. and Khan, Shahjahan (2011) The bivariate noncentral chi-square distribution – a compound distribution approach. Applied Mathematics and Computation, 217 (13). pp. 6237-6247. ISSN 0096-3003

Abstract

This paper proposes the bivariate noncentral chi-square (BNC) distribution by compounding the Poisson probabilities with the bivariate central chi-square distribution. The probability density and cumulative distribution functions of the joint distribution of the two noncentral chi-square variables are derived for arbitrary values of the correlation coefficient, degrees of freedom(s), and noncentrality parameters. Computational procedures to calculate the upper tail probabilities as well as the percentile points for selected values of the parameters, for both equal and unequal degrees of freedom, are discussed. The graphical representation of the distribution for different values of the parameters are provided. Some applications of the distribution are outlined.


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Item Type: Article (Commonwealth Reporting Category C)
Refereed: Yes
Item Status: Live Archive
Additional Information: Permanent restricted access to paper due to publisher copyright restrictions.
Depositing User: Professor Shahjahan Khan
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 29 Jan 2012 23:22
Last Modified: 26 Aug 2014 22:14
Uncontrolled Keywords: bivariate central chi-square distribution; Poisson distribution; compounding method; cumulative distribution; correlation; critical points
Fields of Research (FOR2008): 01 Mathematical Sciences > 0104 Statistics > 010499 Statistics not elsewhere classified
01 Mathematical Sciences > 0104 Statistics > 010405 Statistical Theory
01 Mathematical Sciences > 0104 Statistics > 010404 Probability Theory
Socio-Economic Objective (SEO2008): E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences
Identification Number or DOI: doi: 10.1016/j.amc.2010.12.112
URI: http://eprints.usq.edu.au/id/eprint/20557

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