Extensions of the Freund distribution with applications in reliability theory. (English) Zbl 0551.62070

Shaked, Moshe

Oper. Res. 32, 917-925 (1984).

This paper shows how to unify various well-known generalizations of the Freund distribution by using one simple functional representation. This functional representation has a physical meaning that sheds new light on the meaning of some of these generalizations. Furthermore, using this functional representation, we derive various properties of the Freund distribution and its extensions. In particular, we show that some random variables, which have the Freund distribution or one of its extensions, are positively associated and also belong to some classes of multivariate ”increasing failure rate average” and ”new better than used” distributions. These properties provide bounds for various probabilistic quantities of interest in reliability theory.

MSC:

62N05	Reliability and life testing
62H10	Multivariate distribution of statistics

Keywords:

extensions of Freund distribution; exponential residual lifetime; Weibull; gamma; compounding; mixing; functional representation; increasing failure rate average; new better than used; reliability