Characterizations of Arnold and Strauss' and related bivariate exponential models

JOURNAL OF MULTIVARIATE ANALYSIS

卷:98

Article

Kotz, Samuel ; Navarro, Jorge ; Ruiz, Jose M.

关键词: hazard gradient function;    mean residual life;    conditional moment;    e\xponential model;   

DOI  :  10.1016/j.jmva.2006.09.002

来源: Elsevier

【 摘 要 】

Characterizations of probability distributions is a topic of great popularity in applied probability and reliability literature for over last 30 years. Beside the intrinsic mathematical interest (often related to functional equations) the results in this area are helpful for probabilistic and statistical modelling, especially in engineering and biostatistical problems. A substantial number of characterizations has been devoted to a legion of variants of exponential distributions. The main reliability measures associated with a random vector X are the conditional moment function defined by m(phi)(x) = E (phi(X)vertical bar X >= x) (which is equivalent to the mean residual life function e(x) = m(phi)(x) - x when phi(x) = x) and the and the hazard gradient function h(x) = -del log R(x), where R(x) is the reliability (survival) function, R(x) = Pr(X >= x), and del is the operator del = (partial derivative/partial derivative x(1), partial derivative/partial derivative x(2), ... , partial derivative/partial derivative x(n)). In this paper we study the consequences of a linear relationship between the hazard gradient and the conditional moment functions for continuous bivariate and multivariate distributions. We obtain a general characterization result which is then applied to characterize Arnold and Strauss' bivariate exponential distribution and some related models. (c) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

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