Bayesian estimation of P[Y &lt; X] Based on Record Values from the Lomax Distribution and MCMC Technique

Mahmoud, M. A. W.; EL‐Sagheer, Rashad M.; Soliman, Ahmed A.; Abdellah, Ahmed H.

doi:10.22237/jmasm/1462076640

Cited by 11 publications

(6 citation statements)

References 34 publications

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“…Thus, it is straightforward to construct the first partial derivatives listed in (13). According to Slutsky's theorem, it is easy to verify that…”

Section: Asymptotic Confidence Intervalmentioning

confidence: 99%

“…In a superb monograph published by Kotz et al [1], the various SSR models created before 2001 were described in detail. Although the improvements for the stress-strength models under complete samples have received a great deal of attention see for instance [2][3][4][5][6][7][8][9][10], much focus has been placed on the situation where the data are record values, see [11][12][13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

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Analysis of the Stress–Strength Model Using Uniform Truncated Negative Binomial Distribution under Progressive Type-II Censoring

EL-Sagheer,

Eliwa,

El-Morshedy

et al. 2023

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In this study, we introduce a novel estimation technique for assessing the reliability parameter R=P(Y<X) of the uniform truncated negative binomial distribution (UTNBD) in the context of stress–strength analysis. We base our inferences on the assumption that both the strength (X) and stress (Y) random variables follow a UTNBD with identical first shape and scale parameters. In the presence of a progressive type-II censoring scheme, we employ maximum likelihood, two parametric bootstrap methods, and Bayesian estimation approaches to derive the estimators. Due to the complexity introduced by censoring, the estimators are not available in explicit forms and are instead obtained through numerical approximation techniques. Furthermore, we compute the highest posterior density credible intervals and determine the asymptotic variance-covariance matrix. To assess the performance of our proposed estimators, we conduct a Monte Carlo simulation study and provide a comparative analysis. Finally, we illustrate the practical applicability of our study with an engineering application.

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“…Thus, it is straightforward to construct the first partial derivatives listed in (13). According to Slutsky's theorem, it is easy to verify that…”

Section: Asymptotic Confidence Intervalmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Analysis of the Stress–Strength Model Using Uniform Truncated Negative Binomial Distribution under Progressive Type-II Censoring

EL-Sagheer,

Eliwa,

El-Morshedy

et al. 2023

Axioms

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“…[5] studied exponentiated Lomax Distribution.. The different stress strength model was considered by [6], [7], [8], [9]. Estimation of R = P [X > Y ] for Lomax Distribution with the presence of outliers was discussed by [10].…”

Section: Introductionmentioning

confidence: 99%

Estimation of Stress Strength Reliability P [Y < X < Z] of Lomax Distribution under Different Sampling Scheme

Jacob,

Anjana E. J.

2023

CJAST

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Lomax distribution can be considered as the mixture of exponential and gamma distribution. This distribution is an advantageous lifetime distribution in reliability analysis. The applicability of Lomax distribution is not restricted only to the reliability field, but it has broad applications in Economics, actuarial modelling, queuing problems,biological sciences, etc. Initially, Lomax distribution was proposed by Lomax in 1954, and it is also known as Pareto Type II distribution. Many statistical methods have been developed for this distribution; for a review of Lomax Distribution, see [1] and the references. The stress strength model plays an important role in reliability analysis. The term stress strength was first introduced by [2]. In the context of reliability, R is defined as the probability that the unit strength is greater than stress, that is, R = P (X > Y ), where X is the random strength of the unit, and Y is the instant stress applied to it. Thus, estimation of R is very important in Reliability Analysis.The estimates of R discussed in the context of Lomax distribution are limited to the study of a single stress strength model with upper stress. But in real life, there are situations where we have to consider not only the upper stress Neethu and Anjana; Curr. J. Appl. Sci. Technol., vol. 42, no. 42, pp. 36-66, 2023; Article no.CJAST.107238 but also the lower stress. Accordingly, in the present paper, the estimation of stress strength model R = P (Y < X < Z) represents the situation where the strength X should be greater than stress Y and smaller than stress Z for Lomax distribution, Shrinkage maximum likelihood estimate and Quasi likelihood estimate are obtained both under complete and right censored data. We have considered the asymptotic confidence interval (CI) based on MLE and bootstrap CI for R. Monte Carlo simulation experiments were performed to compare the performance of estimates obtained.

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“…In the literature, there are many life distributions that can be used to estimate R, such as Weibull [5], Pareto [6,11], generalized Pareto [12], exponential [8,13], generalized exponential [14], Lomax [15], unit-half-normal [16], unit-Gompertz [17], and generalized logistic (GL) [18][19][20][21] distributions. The logistic distribution is a symmetric heavy-tailed distribution.…”

Section: Introductionmentioning

confidence: 99%

Generalized Fiducial Inference for the Stress–Strength Reliability of Generalized Logistic Distribution

Yan

Qiao

et al. 2023

Symmetry

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Generalized logistic distribution, as the generalized form of the symmetric logistic distribution, plays an important role in reliability analysis. This article focuses on the statistical inference for the stress–strength parameter R=P(Y<X) of the generalized logistic distribution with the same and different scale parameters. Firstly, we use the frequentist method to construct asymptotic confidence intervals, and adopt the generalized inference method for constructing the generalized point estimators as well as the generalized confidence intervals. Then the generalized fiducial method is applied to construct the fiducial point estimators and the fiducial confidence intervals. Simulation results demonstrate that the generalized fiducial method outperforms other methods in terms of the mean square error, average length, and empirical coverage. Finally, three real datasets are used to illustrate the proposed methods.

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Bayesian estimation of P[Y < X] Based on Record Values from the Lomax Distribution and MCMC Technique

Cited by 11 publications

References 34 publications

Analysis of the Stress–Strength Model Using Uniform Truncated Negative Binomial Distribution under Progressive Type-II Censoring

Analysis of the Stress–Strength Model Using Uniform Truncated Negative Binomial Distribution under Progressive Type-II Censoring

Estimation of Stress Strength Reliability P [Y < X < Z] of Lomax Distribution under Different Sampling Scheme

Generalized Fiducial Inference for the Stress–Strength Reliability of Generalized Logistic Distribution

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