Reliability for Beta Models

Nadarajah, Saralees. "Reliability for Beta Models." Serdica Mathematical Journal 28.3 (2002): 267-282. <http://eudml.org/doc/11562>.

@article{Nadarajah2002,
abstract = {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.},
author = {Nadarajah, Saralees},
journal = {Serdica Mathematical Journal},
keywords = {Beta Distributions; Hypergeometric Functions; Incomplete Beta Function; Reliability; beta distributions; hypergeometric functions; incomplete beta function; reliability},
language = {eng},
number = {3},
pages = {267-282},
publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},
title = {Reliability for Beta Models},
url = {http://eudml.org/doc/11562},
volume = {28},
year = {2002},
}

TY - JOUR
AU - Nadarajah, Saralees
TI - Reliability for Beta Models
JO - Serdica Mathematical Journal
PY - 2002
PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences
VL - 28
IS - 3
SP - 267
EP - 282
AB - 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.
LA - eng
KW - Beta Distributions; Hypergeometric Functions; Incomplete Beta Function; Reliability; beta distributions; hypergeometric functions; incomplete beta function; reliability
UR - http://eudml.org/doc/11562
ER -