Estimation of the Exponential Pareto Distribution’s Parameters under Ranked and Double Ranked Set Sampling Designs

Sabry, M.; Almetwally, Ehab M.

doi:10.18187/pjsor.v17i1.3448

Cited by 12 publications

(2 citation statements)

References 13 publications

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“…In future work, we intend to discuss ranked set sample for PML distribution as Sabry et al [ 38 ], Sabry and Almetwally [ 39 ], Hassan et al [ 31 ], Noor-ul-Amin et al [ 40 ], and Esemen et al [ 41 ]. Also, we intend to discuss the inference of PML distribution based on censored sample as Hassan and Ismail [ 42 ], Almongy et al [ 43 ] Cho and Lee [ 44 ], and Almetwally et al [ 45 ].…”

Section: Discussionmentioning

confidence: 99%

Bayesian and Non-Bayesian Reliability Estimation of Stress-Strength Model for Power-Modified Lindley Distribution

Al-Babtain

Elbatal

Almetwally

2022

Computational Intelligence and Neuroscience

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A two-parameter continuous distribution, namely, power-modified Lindley (PML), is proposed. Various structural properties of the new distribution, including moments, moment-generating function, conditional moments, mean deviations, mean residual lifetime, and mean past lifetime, are provided. The reliability of a system is discussed when the strength of the system and the stress imposed on it are independent. Maximum-likelihood estimation of the parameters and their estimated asymptotic standard errors are derived. Bayesian estimation methods of the parameters with independent gamma prior are discussed based on symmetric and asymmetric loss functions. We proposed using the MCMC technique with the Metropolis–Hastings algorithm to approximate the posteriors of the stress-strength parameters for Bayesian calculations. The confidence interval for likelihood and the Bayesian estimation method is obtained for the parameter of the model and stress-strength reliability. We prove empirically the importance and flexibility of the new distribution in modeling with real data applications.

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Section: Discussionmentioning

confidence: 99%

Bayesian and Non-Bayesian Reliability Estimation of Stress-Strength Model for Power-Modified Lindley Distribution

Al-Babtain

Elbatal

Almetwally

2022

Computational Intelligence and Neuroscience

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“…The derivation of the parameter estimation based on Simple Random Sampling and Ranked Set Sampling for Gumbel distribution and logistic distribution are discussed by [20,21]. The derivation of the likelihood function for parameter estimation based on double-ranked set sampling (DRSS) designs were used by [22] for the estimation of the parameters of the power-generalized Weibull distribution. The authors of [23] derived the estimate of the finite population total under Ranked Set Sampling Without Replacement (RSSWOR), employing the model relationship, especially Gamma Population Model (GPM), between the study and auxiliary variables.…”

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confidence: 99%

Parameter Estimation of the Exponentiated Pareto Distribution Using Ranked Set Sampling and Simple Random Sampling

Khamnei

Meidutė‐Kavaliauskienė

Fathi

et al. 2022

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In this paper, we have considered that ranked set sampling is able to estimate the parameters of exponentiated Pareto distribution. The method with which the maximum likelihood estimators for the parameters of exponentiated Pareto distribution is studied is numerical since there is no presence or possibility of a closed-form at the hands of estimators or any other intellectual. The numerical approach is a well-suited one for this study as there has been struggles in achieving it with any other technique. In order to compare the different sampling methods, simulation studies are performed as the main technique. As for the illustrative purposes, analysis of a simulated dataset is desired for the objective of the presentation. The conclusion that we can reach based on these is that the estimators based on the ranked set sample have far better efficiency than the simple random sample at the same sample size.

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Statistical inference for a novel distribution using ranked set sampling with applications

Aljohani

2024

Heliyon

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Estimation of the Exponential Pareto Distribution’s Parameters under Ranked and Double Ranked Set Sampling Designs

Cited by 12 publications

References 13 publications

Bayesian and Non-Bayesian Reliability Estimation of Stress-Strength Model for Power-Modified Lindley Distribution

Bayesian and Non-Bayesian Reliability Estimation of Stress-Strength Model for Power-Modified Lindley Distribution

Parameter Estimation of the Exponentiated Pareto Distribution Using Ranked Set Sampling and Simple Random Sampling

Statistical inference for a novel distribution using ranked set sampling with applications

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