### 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 |
---|---|

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 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

**The construction of new bivariate exponential distributions from a Bayesian perspective.** / Hayakawa, Yu.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - The construction of new bivariate exponential distributions from a Bayesian perspective

AU - Hayakawa, Yu

PY - 1994

Y1 - 1994

N2 - 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.

AB - 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.

KW - Freund distribution

KW - Friday–Patil distribution

KW - l-isotropy

KW - Marshall–Olkin distribution

KW - Principle of indifference

UR - http://www.scopus.com/inward/record.url?scp=21844491819&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21844491819&partnerID=8YFLogxK

U2 - 10.1080/01621459.1994.10476840

DO - 10.1080/01621459.1994.10476840

M3 - Article

AN - SCOPUS:21844491819

VL - 89

SP - 1044

EP - 1049

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

SN - 0162-1459

IS - 427

ER -