An Alternative to the Marshall-Olkin Family of Distributions: Bootstrap, Regression and Applications

Chesneau, Christophe; Karakaya, Kadir; Bakouch, Hassan S.; Kuş, Çoşkun

doi:10.1007/s42967-021-00167-w

Cited by 4 publications

(4 citation statements)

References 27 publications

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“…There are many lifetime distributions in the literature obtained by means of the MO distribution family, such as the MO Frechet distribution [ 29 ], beta MO distribution family [ 30 ], MO generalized exponential distribution [ 31 ], MO alpha power distribution [ 32 ], and Weibull MO family [ 33 ]. Chesneau et al [ 34 ] proposed a generalization of the MO family, which they called the generalized Marshall-Olkin (GMO) distribution. It is remarkable that their obtained model is more flexible than the original MO distribution family.…”

Section: Introductionmentioning

confidence: 99%

Generalized Marshall-Olkin exponentiated exponential distribution: Properties and applications

Ozkan

Şimşek

2023

PLoS ONE

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In this study, we propose a generalized Marshall-Olkin exponentiated exponential distribution as a submodel of the family of generalized Marshall-Olkin distribution. Some statistical properties of the proposed distribution are examined such as moments, the moment-generating function, incomplete moment, and Lorenz and Bonferroni curves. We give five estimators for the unknown parameters of the proposed distribution based on maximum likelihood, least squares, weighted least squares, and the Anderson-Darling and Cramer-von Mises methods of estimation. To investigate the finite sample properties of the estimators, a comprehensive Monte Carlo simulation study is conducted for the models with three sets of randomly selected parameter values. Finally, four different real data applications are presented to demonstrate the usefulness of the proposed distribution in real life.

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Section: Introductionmentioning

confidence: 99%

Generalized Marshall-Olkin exponentiated exponential distribution: Properties and applications

Ozkan

Şimşek

2023

PLoS ONE

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“…After the later papers by Efron and Gong (1983), Efron and Tibshirani (1986), Diaconis and Efron (1983) that the statistical and scientific community began began to take these ideas into account, to appreciate the extensions and broad applicability of the methods, and to recognize their importance (Chernick 2008). There are so many studies used the bootstrap method with a view to make statistical inference by the help of confidence intervals: see also Efron and Tibshirani (1986), Diaconis and Efron (1983), Efron (1987), Carpenter, and Bithell (2000), Park (2011), DiCiccio andEfron (1996), DiCiccio and Tibshirani (1987), Efron and Tibshirani (1993), Chesneau et al (2022) and Akdoğan (2022).…”

Section: Introductionmentioning

confidence: 99%

Shrinkage Estimation and Bootstrap Confidence Interval for Scale Parameter of Laplace Distribution

ÖZDEMİR,

EBEGİL

2023

Afyon Kocatepe University Journal of Sciences and Engineering

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In this study, a biased estimator is proposed for the scale parameter of Laplace distribution. First, it is theoretically shown that the mean square error of the biased estimator is smaller than that of the maximum likelihood estimator. Then the maximum likelihood estimator is compared with the obtained biased estimator by means of a simulation study using the relative efficiency of these estimators. In addition, confidence intervals are constructed for the scale parameter of Laplace distribution with bootstrap method in order to compare them with each other in a different way.

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“…The exponentiated Marshall Olkin family distribution is used to provide consistently better fits than other generated models under the same baseline distribution. The Marshall Olkin family distribution is introduced and discussed in many papers in literature such as [20][21][22][23][24][25][26].…”

Section: Introductionmentioning

confidence: 99%

Inference on the stress strength reliability with exponentiated generalized Marshall Olkin-G distribution

Salah Youssef Temraz

2023

PLoS ONE

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In this paper, an inference on stress-strength reliability model is introduced in case of the exponentiated generalized Marshall Olkin G family of distributions. The maximum likelihood estimator of the stress-strength reliability function is deduced. An asymptotic confidence and bootstrap confidence intervals for the stress-strength reliability function are derived. A Bayesian inference is introduced for the stress-strength reliability. A simulation is introduced to obtain the maximum likelihood and Bayesian estimates for the stress strength reliability. Real data applications are provided to show the results for the stress-strength model and compare the exponentiated generalized Marshall Olkin-G distribution with other distributions.

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An Alternative to the Marshall-Olkin Family of Distributions: Bootstrap, Regression and Applications

Cited by 4 publications

References 27 publications

Generalized Marshall-Olkin exponentiated exponential distribution: Properties and applications

Generalized Marshall-Olkin exponentiated exponential distribution: Properties and applications

Shrinkage Estimation and Bootstrap Confidence Interval for Scale Parameter of Laplace Distribution

Inference on the stress strength reliability with exponentiated generalized Marshall Olkin-G distribution

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