TY - JOUR

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

AU - Hayakawa, Yu

N1 - Funding Information:
* Yu Hayakawa is Lecturer, Institute of Statistics and Operations Research, Victoria University of Wellington, New Zealand. This research was supported by grants to the University of California at Berkeley by the Army Research Office. The author is very grateful for the helpful comments of Richard E. Barlow, Max B. Mendel, Deborah A. Nolan, Roger M. Cooke, and Ole Hesselager. The author also thanks the editor, the associate editor, and the referees for useful comments and suggestions that led to improvements in this article.

PY - 1994/9

Y1 - 1994/9

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 - Marshall–Olkin distribution

KW - Principle of indifference

KW - l-isotropy

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U2 - 10.1080/01621459.1994.10476840

DO - 10.1080/01621459.1994.10476840

M3 - Article

AN - SCOPUS:21844491819

VL - 89

SP - 1044

EP - 1049

JO - Quarterly Publications of the American Statistical Association

JF - Quarterly Publications of the American Statistical Association

SN - 0162-1459

IS - 427

ER -