### Abstract

We use an economic approach of Mendel to derive new bivariate exponential lifetime distributions. Features distinguishing this approach from the existing ones are (1) it makes use of the principle of indifference; (2) our parameter of interest is a measurable function of observable quantities; (3) the assessment of the probability measure for random lifetimes is performed by assessing that for random lifetime costs with a change of variables; and (4) characterization properties other than the bivariate loss-of-memory property are used to construct distributions. For the infinite population case, our distributions correspond to mixtures of existing bivariate exponential distributions such as the Freund distribution, the Marshall–Olkin distribution, and the Friday–Patil distribution. Moreover, a family of natural conjugate priors for Bayesian Freund (-type) bivariate exponential distributions is discussed.

Original language | English |
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Pages (from-to) | 1044-1049 |

Number of pages | 6 |

Journal | Journal of the American Statistical Association |

Volume | 89 |

Issue number | 427 |

DOIs | |

Publication status | Published - 1994 Sep |

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### Keywords

- Freund distribution
- Friday–Patil distribution
- Marshall–Olkin distribution
- Principle of indifference
- l-isotropy

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty