Jones, M. C.
(2002).
*t* distribution with marginals on different degrees of freedom.*Statistics & Probability Letters*, 56(2) pp. 163–170.

DOI (Digital Object Identifier) Link: | http://doi.org/10.1016/S0167-7152(01)00180-8 |
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## Abstract

Let *Z*_{1},*Z*_{2} and *W*_{1},*W*_{2} be mutually independent random variables, each *Z*_{i} following the standard normal distribution and *W*_{i} following the chi-squared distribution on *n*_{i} degrees of freedom. Then, the pair of random variables {√*n*_{1}*Z*_{1}/√*W*_{1}, √*n*_{1}*Z*_{2}/√*W*_{1}} has the bivariate spherically symmetric *t* distribution; this has both marginals the same, namely Student's *t* distributions on *n*_{1} degrees of freedom. In this paper, we study the joint distribution of {√ν_{1}*Z*_{1}/√*W*_{1}, √ν_{2}*Z*_{2}/√*W*_{1}+*W*_{2}} where ν_{1}=*n*_{1}, ν_{2}=*n*_{1}+*n*_{2}. This bivariate distribution has marginal distributions which are Student *t* distributions on different degrees of freedom if ν_{1}≠ν_{2}. The marginals remain uncorrelated, as in the spherically symmetric case, but are also by no means independent.

Item Type: | Journal Article |
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Copyright Holders: | 2002 Elsevier Science B.V. |

ISSN: | 0167-7152 |

Extra Information: | Please note the mathematical notation in the above abstract may not be accurate due to font limitations. |

Keywords: | bivariate distribution; spherical symmetry; student's t distribution |

Academic Unit/Department: | Mathematics, Computing and Technology > Mathematics and Statistics Mathematics, Computing and Technology |

Item ID: | 22662 |

Depositing User: | Sarah Frain |

Date Deposited: | 11 Aug 2010 10:51 |

Last Modified: | 15 Jan 2016 14:47 |

URI: | http://oro.open.ac.uk/id/eprint/22662 |

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