Estimation ofP(Y &lt; X) for the Three-Parameter Generalized Exponential Distribution

Raqab, Mohammad Z.; Madi, Mohamed T.; Kundu, Debasis

doi:10.1080/03610920802162664

Cited by 116 publications

(48 citation statements)

References 13 publications

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“…The first data from Raqab et al (2008) These data represent the tensile strength data measured in GPa for singlecarbon fibers. Alzaatreh and Knight (2013) fitted these data to the gammahalf normal, half normal, generalized half-normal and beta generalized half normal distributions.…”

Section: Applicationsmentioning

confidence: 99%

The Lomax-Exponential Distribution, Some Properties and Applications

Golzar¹,

Ganji²,

Bevrani³

2017

JSRI

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Abstract. The exponential distribution is a popular model in applications to real data. We propose a new extension of this distribution, called the Lomax-exponential distribution, which presents greater flexibility to the model. Also there is a simple relation between the Lomax-exponential distribution and the Lomax distribution. Results for moment, limit behavior, hazard function, Shannon entropy and order statistic are provided. To estimate the model parameters, the method of maximum likelihood and Bayse estimations are proposed. Two data sets are used to illustrate the applicability of the Lomax-exponential distribution.

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Section: Applicationsmentioning

confidence: 99%

The Lomax-Exponential Distribution, Some Properties and Applications

Golzar¹,

Ganji²,

Bevrani³

2017

JSRI

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“…For a fixed scale parameter value, the skewness gradually decreases as the shape parameter increases. Kundu and Gupta [6] and Raqab et al [7] considered maximum likelihood estimation of R when X and Y are independent EE(α 1 , β 1 ) and EE(α 2 , β 2 ) distributed random variables and where β 1 and β 2 are assumed to be the same. Then R = α 1 α 1 +α 2 .…”

Section: Problemmentioning

confidence: 99%

A Penalized Likelihood Approach to Parameter Estimation with Integral Reliability Constraints

Smith

Wang

Zhou

2015

Entropy

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Stress-strength reliability problems arise frequently in applied statistics and related fields. Often they involve two independent and possibly small samples of measurements on strength and breakdown pressures (stress). The goal of the researcher is to use the measurements to obtain inference on reliability, which is the probability that stress will exceed strength. This paper addresses the case where reliability is expressed in terms of an integral which has no closed form solution and where the number of observed values on stress and strength is small. We find that the Lagrange approach to estimating constrained likelihood, necessary for inference, often performs poorly. We introduce a penalized likelihood method and it appears to always work well. We use third order likelihood methods to partially offset the issue of small samples. The proposed method is applied to draw inferences on reliability in stress-strength problems with independent exponentiated exponential distributions. Simulation studies are carried out to assess the accuracy of the proposed method and to compare it with some standard asymptotic methods.

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“…Inference regarding P (Y < X), defining the reliability of the system, has been widely discussed in literature, when Xand Y are assumed to be independent random variables. See, for example, Basu (1964), Downtown (1973), Tong (1974Tong ( , 1977, Kelley, Kelley, and Suchany (1976), Beg (1980), Iwase (1987), McCool (1991), Ivshin (1996), Ali, Woo, and Pal (2004); Woo (2005, 2010), Woo (2005a, 2005b), Pal, Ali, and Woo (2005), Raqab and Kundu (2005), and Raqab, Madi, and Kundu (2008). Besides, system reliability, P (Y < X) finds importance in other fields too.…”

Section: Introductionmentioning

confidence: 99%

Estimation of P(Y < X) in a Four-Parameter Generalized Gamma Distribution

Ali

Pal

Woo

2016

AJS

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In this paper we consider estimation of R = P (Y < X), when X and Y are distributed as two independent four-parameter generalized gamma random variables with same location and scale parameters. A modified maximum likelihood method and a Bayesian technique have been used to estimate R on the basis of independent samples. As the Bayes estimator cannot be obtained in a closed form, it has been implemented using importance sampling procedure. A simulation study has also been carried out to compare the two methods.Zusammenfassung: In diesem Beitrag betrachten wir die Schätzung von R = P (Y < X), wenn die beiden unabhängigen Zufallsvariablen X und Y aus einer Vier-Parameter generalisierten Gammaverteilung mit gleichen Lokations-und Skalen-Parametern stammen. Eine modifizierte MaximumLikelihood Methode und eine Bayes-Technik wurden verwendet, um R auf der Grundlage von unabhängigen Stichproben zu schätzen. Da der BayesSchätzer nicht in geschlossener Form dargestellt werden kann, wurde dieser mittels einer Importance Sampling Prozedur implementiert. Eine Simulationsstudie wurde ebenfalls durchgeführt, um beide Methoden zu vergleichen.

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Estimation ofP(Y < X) for the Three-Parameter Generalized Exponential Distribution

Cited by 116 publications

References 13 publications

The Lomax-Exponential Distribution, Some Properties and Applications

The Lomax-Exponential Distribution, Some Properties and Applications

A Penalized Likelihood Approach to Parameter Estimation with Integral Reliability Constraints

Estimation of P(Y < X) in a Four-Parameter Generalized Gamma Distribution

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