Geodesic
Reliability for Beta Models
Serdica Mathematical Journal, Tome 28 (2002) no. 3, pp. 267-282 Cet article a éte moissonné depuis la source Bulgarian Digital Mathematics Library

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In the area of stress-strength models there has been a large amount of work as regards estimation of the reliability R = Pr(X2 X1 ) when X1 and X2 are independent random variables belonging to the same univariate family of distributions. The algebraic form for R = Pr(X2 X1 ) has been worked out for the majority of the well-known distributions including Normal, uniform, exponential, gamma, weibull and pareto. However, there are still many other distributions for which the form of R is not known. We have identified at least some 30 distributions with no known form for R. In this paper we consider some of these distributions and derive the corresponding forms for the reliability R. The calculations involve the use of various special functions.
Keywords: Beta Distributions, Hypergeometric Functions, Incomplete Beta Function, Reliability 
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     author = {Nadarajah, Saralees},
     title = {Reliability for {Beta} {Models}},
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     language = {en},
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Nadarajah, Saralees. Reliability for Beta Models. Serdica Mathematical Journal, Tome 28 (2002) no. 3, pp. 267-282. http://geodesic.mathdoc.fr/item/SMJ2_2002_28_3_a7/