The construction of new bivariate exponential distributions from a Bayesian perspective

Research output: Contribution to journalArticle

13 Citations (Scopus)

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 languageEnglish
Pages (from-to)1044-1049
Number of pages6
JournalJournal of the American Statistical Association
Volume89
Issue number427
DOIs
Publication statusPublished - 1994
Externally publishedYes

Fingerprint

Bivariate Exponential Distribution
Lifetime
Bivariate Exponential
Conjugate prior
Lifetime Distribution
Change of Variables
Measurable function
Exponential distribution
Probability Measure
Economics
Costs

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.

In: Journal of the American Statistical Association, Vol. 89, No. 427, 1994, p. 1044-1049.

Research output: Contribution to journalArticle

@article{4b8e1471740a408dbc52110ddde7a2bb,
title = "The construction of new bivariate exponential distributions from a Bayesian perspective",
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.",
keywords = "Freund distribution, Friday–Patil distribution, l-isotropy, Marshall–Olkin distribution, Principle of indifference",
author = "Yu Hayakawa",
year = "1994",
doi = "10.1080/01621459.1994.10476840",
language = "English",
volume = "89",
pages = "1044--1049",
journal = "Journal of the American Statistical Association",
issn = "0162-1459",
publisher = "Taylor and Francis Ltd.",
number = "427",

}

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 -