
In this paper, we give an identity based on conditional mean to determine the failure rate of a distribution. Some well-known characterizations are deduced as special cases. We also present various applications of the identity. By extending this to the bivariate case, we obtain a class of distributions with a specified form of failure rate. Finally we study the properties and the applications of the bivariate model.
Reliability and life testing, Characterization and structure theory of statistical distributions, reliability analysis, Characterization and structure theory for multivariate probability distributions; copulas, conditional mean, bivariate distribution
Reliability and life testing, Characterization and structure theory of statistical distributions, reliability analysis, Characterization and structure theory for multivariate probability distributions; copulas, conditional mean, bivariate distribution
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