Characterizing the Multivariate Exponential Distributions
Abstract
The main majority of the multivariate exponential distributions rise in the dependability framework one approach or any other approach. When we consider of dependability, we have in concentration the death of a living organism or the failure of an element. We particularly consider of time lapsing between the equipment being put into service and its failure. In the multivariate or bivariate framework, we are attention with dependencies between binary failure times, such as those of two components of a biological system, mechanical or electrical.
Multivariate and bivariate exponential distributions have assisted as approachable “substitute arena” for those elaborate in applied or/and theoretical features of multivariate distributions. The capacity on the exponential distribution organized by Balakrishnan and Basu (1995) delivers sufficient testimony to this statement.
In this article, a characterization of the exponential-distribution based on the assets of the bivariate exponential is studied. The outcome methods a sort of multivariate correspondent of the characterization of the bivariate-exponential-distribution.
Even though various methods of bivariate-exponential-distributions such those of Marshall and Olkin (1967), Freund (1961), Block and Basu (1974) and Gumbel (1960) will be literature, how far these distributions can be considered by characters of analogous to the outcomes in the bivariate-exponential-distribution.
At the start we extant a comprehensive conversation on bivariate-exponential-distributions, relating numerous various methods that have been planned in the literature, their applications, properties and inferential concerns. Following, we review different signs of progress on multivariate-exponential-distributions. It should be stated that while this part includes many outcomes from the capacious literature on this subject, it can by no means be considered as comprehensive attention of this active area of investigation.
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