# Reliability for Beta Models

Serdica Mathematical Journal (2002)

- Volume: 28, Issue: 3, page 267-282
- ISSN: 1310-6600

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topNadarajah, 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 -

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