Bayesian and Classical Estimation of the Inverse Pareto Distribution and Its Application to Strength-Stress Models

Guo, Liu; Gui, Wenhao

doi:10.1080/01966324.2017.1383217

Cited by 12 publications

(11 citation statements)

References 16 publications

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“…This real data set contains the failure times (in hours) of one plane's ac system from a pair of real data sets collected by Bain and Engelhardt [30]. Moreover, Guo and Gui [31] demonstrated that these data sets closely matched the inverse Pareto distribution. For further proceeding, before using these data, we ran Kolmogorov-Smirnov (KS) goodness of fit tests to see if they followed the Pareto distribution or not.…”

Section: Numerical Examplementioning

confidence: 98%

Classical and Bayesian Inference Using Type-II Unified Progressive Hybrid Censored Samples for Pareto Model

Nagy

Alrasheedi

2022

Applied Bionics and Biomechanics

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In the lifetime and reliability experiments, the censored samples play a fundamental and important role in order to control time and cost. The researchers developed the censored sample schemes to solve the problems that arise by applying the previous methods. Recently, Górny and Cramer (2018) proposed a new general type of censored sample called Type-II unified progressive hybrid censored sample. In this paper, we present an overview of the Type-II unified progressive hybrid censored sample. We used this censored sample to compute the maximum likelihood estimates of unknown parameters from the Pareto distribution, as well as Bayesian estimates for unknown parameters under three different error loss functions. The point and interval Bayesian predictions one- and two-sample Bayesian predictions from the Pareto distribution are shown. Simulation studies are carried out to compare the efficacy of the various inference approaches. Finally, real data sets are examined to determine the applicability of the proposed model and various estimating approaches.

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Section: Numerical Examplementioning

confidence: 98%

Classical and Bayesian Inference Using Type-II Unified Progressive Hybrid Censored Samples for Pareto Model

Nagy

Alrasheedi

2022

Applied Bionics and Biomechanics

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“…To analyze such data IPD may be appropriate, see [ 18 ]. In reliability engineering, the application of the IPD lifetime model has been discussed by [ 4 ] with the help of the failure time of the air conditioning system of two airplanes. Also, a number of research papers have described the popularity of the IPD lifetime model.…”

Section: Model Description and Ssrmentioning

confidence: 99%

On estimation of P(Y < X) for inverse Pareto distribution based on progressively first failure censored data

Alharbi,

Garg,

Kumar

et al. 2023

PLoS ONE

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The stress-strength reliability (SSR) model ϕ = P(Y < X) is used in numerous disciplines like reliability engineering, quality control, medical studies, and many more to assess the strength and stresses of the systems. Here, we assume X and Y both are independent random variables of progressively first failure censored (PFFC) data following inverse Pareto distribution (IPD) as stress and strength, respectively. This article deals with the estimation of SSR from both classical and Bayesian paradigms. In the case of a classical point of view, the SSR is computed using two estimation methods: maximum product spacing (MPS) and maximum likelihood (ML) estimators. Also, derived interval estimates of SSR based on ML estimate. The Bayes estimate of SSR is computed using the Markov chain Monte Carlo (MCMC) approximation procedure with a squared error loss function (SELF) based on gamma informative priors for the Bayesian paradigm. To demonstrate the relevance of the different estimates and the censoring schemes, an extensive simulation study and two pairs of real-data applications are discussed.

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“…The fit of the proposed APP distribution is compared with several other competitive models namely Basic Pareto, Pareto distribution by [35], Genaralized Pareto distibution by [22], Kumaraswamy Pareto distribution by [29], Exponentiated Generalized Pareto Distribution by [14] and Inverse Pareto distribution [36] with the following pdfs.…”

Section: Parameters Estimationmentioning

confidence: 99%

Alpha-Power Pareto distribution: Its properties and applications

et al. 2019

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In Statistical theory, inclusion of an additional parameter to standard distributions is a usual practice. In this study, a new distribution referred to as Alpha-Power Pareto distribution is introduced by including an extra parameter. Several properties of the proposed distribution, including moment generating function, mode, quantiles, entropies, mean residual life function, stochastic orders and order statistics are obtained. Parameters of the proposed distribution have been estimated using maximum likelihood estimation technique. Two real datasets have been considered to examine the usefulness of the proposed distribution. It has been observed that the proposed distribution outperforms different variants of Pareto distribution on the basis of model selection criteria.

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Bayesian and Classical Estimation of the Inverse Pareto Distribution and Its Application to Strength-Stress Models

Cited by 12 publications

References 16 publications

Classical and Bayesian Inference Using Type-II Unified Progressive Hybrid Censored Samples for Pareto Model

Classical and Bayesian Inference Using Type-II Unified Progressive Hybrid Censored Samples for Pareto Model

On estimation of P(Y < X) for inverse Pareto distribution based on progressively first failure censored data

Alpha-Power Pareto distribution: Its properties and applications

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