Identifiability of the multinormal and other distributions under competing risks model

A. P. Basu and J. K. Ghosh

Journal of Multivariate Analysis, 1978, vol. 8, issue 3, 413-429

Abstract: Let X1, X2 ,..., Xp be p random variables with joint distribution function F(x1 ,..., xp). Let Z = min(X1, X2 ,..., Xp) and I = i if Z = Xi. In this paper the problem of identifying the distribution function F(x1 ,..., xp), given the distribution Z or that of the identified minimum (Z, I), has been considered when F is a multivariate normal distribution. For the case p = 2, the problem is completely solved. If p = 3 and the distribution of (Z, I) is given, we get a partial solution allowing us to identify the independent case. These results seem to be highly nontrivial and depend upon Liouville's result that the (univariate) normal distribution function is a nonelementary function. Some other examples are given including the bivariate exponential distribution of Marshall and Olkin, Gumbel, and the absolutely continuous bivariate exponential extension of Block and Basu.

Keywords: Identifiability; multivariate; normal; distribution; competing; risk; series; system; distribution; of; minimum (search for similar items in EconPapers)
Date: 1978
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Citations: View citations in EconPapers (30)

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