ON SOME NEW CLASSES OF MULTIVARIATE PROBABILITY DISTRIBUTIONS (original) (raw)

Abstract

New Classes of transformations on the Euclidean n-space R n are applied to sets of n (n = 2, 3, …) independent random variables T 1 , …, T n. Basically two cases are considered: 1) the random variables are all Weibullian, and 2) they are all gamma. The transformations, when applied to the random vectors (T 1 , …, T n), produce, as outputs, r. vectors (X 1 , …, X n) whose joint probability densities are investigated. The new probability densities of (X 1 , …, X n) produced by the Weibullian input r. variables T 1 , …, T n are called " pseudoWeibullians " , and the other " pseudogammas ". The origin and the basis for new methods of pdfs construction is set of problems associated with multicomponent system reliability modeling. In this context the random variables X 1 , …, X n are used to represent the system components life times.

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