Jones, M.C.
(2007).
*International Statistical Review*, 75(1) pp. 58–69.

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## Abstract

Univariate continuous distributions have three possible types of support exemplified by: the whole real line, R, the semi-finite interval R+ = (0, infinity) and the bounded interval (0,1). This paper is about connecting distributions on these supports via 'natural' simple transformations in such a way that tail properties are preserved. In particular, this work is focussed on the case where the tails (at +/-infinity) of densities are heavy, decreasing as a (negative) power of their argument; connections are then especially elegant. At boundaries (0 and 1), densities behave conformably with a directly related dependence on power of argument. The transformation from (0,1) to R+ is the standard odds transformation. The transformation from R+ to R is a novel identity-minus-reciprocal transformation. The main points of contact with existing distributions are with the transformations involved in the Birnbaum-Saunders distribution and, especially, the Johnson family of distributions. Relationships between. various other existing and newly proposed distributions are explored.

Item Type: | Journal Item |
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ISSN: | 0306-7734 |

Keywords: | Distribution; Probability theory; Transformations; Mathematics; Numerical analysis; Statistics; Boundaries; Birnbaum–Saunders distribution; Johnson distributions; Power tails |

Academic Unit/School: | Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics Faculty of Science, Technology, Engineering and Mathematics (STEM) |

Item ID: | 15622 |

Depositing User: | Colin Smith |

Date Deposited: | 27 Apr 2009 09:22 |

Last Modified: | 04 Oct 2016 10:20 |

URI: | http://oro.open.ac.uk/id/eprint/15622 |

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