Yunus, Rossita M. and Khan, Shahjahan ORCID: https://orcid.org/0000-0002-0446-086X
(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) |
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Refereed: | Yes |

Item Status: | Live Archive |

Additional Information: | Permanent restricted access to paper due to publisher copyright restrictions. |

Faculty/School / Institute/Centre: | Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013) |

Faculty/School / Institute/Centre: | Historic - Faculty of Sciences - Department of Maths and Computing (Up to 30 Jun 2013) |

Date Deposited: | 29 Jan 2012 23:22 |

Last Modified: | 28 Apr 2017 04:51 |

Uncontrolled Keywords: | bivariate central chi-square distribution; Poisson distribution; compounding method; cumulative distribution; correlation; critical points |

Fields of Research (2008): | 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 |

Fields of Research (2020): | 49 MATHEMATICAL SCIENCES > 4905 Statistics > 490599 Statistics not elsewhere classified 49 MATHEMATICAL SCIENCES > 4905 Statistics > 490509 Statistical theory 49 MATHEMATICAL SCIENCES > 4905 Statistics > 490506 Probability theory |

Socio-Economic Objectives (2008): | E Expanding Knowledge > 97 Expanding Knowledge > 970101 Expanding Knowledge in the Mathematical Sciences |

Identification Number or DOI: | https://doi.org/10.1016/j.amc.2010.12.112 |

URI: | http://eprints.usq.edu.au/id/eprint/20557 |

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