Modeling engineering data using extended power-Lindley distribution: Properties and estimation methods

Al-Babtain, Abdulhakim A.; Kumar, Devendra; Gemeay, Ahmed M.; Dey, Sanku; Afify, Ahmed Z.

doi:10.1016/j.jksus.2021.101582

Cited by 6 publications

(3 citation statements)

References 24 publications

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“…Additionally, the TIEx-W parameters are estimated by using several estimation methods and their performance is explored by detailed simulations for small and large samples. Many authors have addressed different estimators to estimate the parameters of generalized models such as the Weibull–Marshall–Olkin power-Lindley distribution by [ 12 ] and the Marshall–Olkin–Weibull exponential distribution by [ 13 ].…”

Section: Introductionmentioning

confidence: 99%

Classical and Bayesian estimation for type-I extended-F family with an actuarial application

et al. 2023

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In this work, a new flexible class, called the type-I extended-F family, is proposed. A special sub-model of the proposed class, called type-I extended-Weibull (TIEx-W) distribution, is explored in detail. Basic properties of the TIEx-W distribution are provided. The parameters of the TIEx-W distribution are obtained by eight classical methods of estimation. The performance of these estimators is explored using Monte Carlo simulation results for small and large samples. Besides, the Bayesian estimation of the model parameters under different loss functions for the real data set is also provided. The importance and flexibility of the TIEx-W model are illustrated by analyzing an insurance data. The real-life insurance data illustrates that the TIEx-W distribution provides better fit as compared to competing models such as Lindley–Weibull, exponentiated Weibull, Kumaraswamy–Weibull, α logarithmic transformed Weibull, and beta Weibull distributions, among others.

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Section: Introductionmentioning

confidence: 99%

Classical and Bayesian estimation for type-I extended-F family with an actuarial application

et al. 2023

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“…based on GG distributions can be done by using our suggested AMLEs for GG distribution parameters in future works. For more readind see the following references [16][17][18][19][20].…”

Section: Discussionmentioning

confidence: 99%

Approximate Maximum Likelihood Estimations for the Parameters of the Generalized Gudermannian Distribution and Its Characterizations

Rasekhi

Saber

Hamedani

et al. 2022

Journal of Mathematics

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Generalized Gudermannian distribution is a symmetric distribution with location and scale parameters as an alternative to the well-known symmetric distributions such as normal, Laplace, and Cauchy. This distribution has a simple closed form for the probability density function (pdf) and cumulative distribution function (cdf) and is more flexible than normal distribution based on kurtosis criterion. Certain characterizations of this distribution are presented. For this distribution, due to the nonlinear form of the likelihood equations, the maximum likelihood estimations (MLEs) of the location and scale parameters do not have closed forms and need a numerical approximation method with suitable starting values. A simple method of deriving explicit estimators by approximating the likelihood equations is presented. The bias and variance of these estimators are examined numerically and are shown that these estimators are as efficient as the maximum likelihood estimators. Some pivotal quantities are proposed for finding confidence intervals for location and scale parameters based on asymptotic normality. From the coverage probability, the MLEs do not work well especially for the small sample sizes; thus, to improve the coverage probability, simulated percentiles based on the Monte Carlo method are used. Finally, a real data set is presented to illustrate the suggested method and its inference related to this data set.

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“…The literature on distribution theory contains a series of probability distributions for analyzing and predicting real phenomena in various applied areas, such as the healthcare and biomedical sectors, engineering sector, actuarial and management sciences, education, and hydrology [1][2][3][4][5][6][7][8]. However, no particular probability model is appropriate for analyzing and predicting every phenomenon.…”

Section: Introductionmentioning

confidence: 99%

A Weighted Cosine-G Family of Distributions: Properties and Illustration Using Time-to-Event Data

Odhah,

Alshanbari,

Ahmad

et al. 2023

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Modeling and predicting time-to-event phenomena in engineering, sports, and medical sectors are very crucial. Numerous models have been proposed for modeling such types of data sets. These models are introduced by adding one or more parameters to the traditional distributions. The addition of new parameters to the traditional distributions leads to serious issues, such as estimation consequences and re-parametrization problems. To avoid such problems, this paper introduces a new method for generating new probability distributions without any additional parameters. The proposed method may be called a weighted cosine-G family of distributions. Different distributional properties of the weighted cosine-G family, along with the maximum likelihood estimators, are obtained. A special model of the weighted cosine-G family, by utilizing the Weibull model, is considered. The special model of the weighted cosine-G family may be called a weighted cosine-Weibull distribution. A simulation study of the weighted cosine-Weibull model is conducted to evaluate the performances of its estimators. Finally, the applications of the weighted cosine-Weibull distribution are shown by considering three data sets related to the time-to-event phenomena.

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Modeling engineering data using extended power-Lindley distribution: Properties and estimation methods

Cited by 6 publications

References 24 publications

Classical and Bayesian estimation for type-I extended-F family with an actuarial application

Classical and Bayesian estimation for type-I extended-F family with an actuarial application

Approximate Maximum Likelihood Estimations for the Parameters of the Generalized Gudermannian Distribution and Its Characterizations

A Weighted Cosine-G Family of Distributions: Properties and Illustration Using Time-to-Event Data

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