Power-Modified Kies-Exponential Distribution: Properties, Classical and Bayesian Inference with an Application to Engineering Data

Afify, Ahmed Z.; Gemeay, Ahmed M.; Alfaer, Nada M.; Cordeiro, Gauss M.; Hussam, Eslam

doi:10.3390/e24070883

Cited by 23 publications

(7 citation statements)

References 20 publications

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“…The results are reported in the second part of Table 2. We can see that the two-, three-, and four-component distributions approximate similar domains, namely near the interval (1,9). Also, the returned errors are statistically indistinguishable.…”

Section: Unemployment Insurance Issuesmentioning

confidence: 70%

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On min- and max-Kies families: distributional properties and saturation in Hausdorff sense

Zaevski,

Kyurkchiev

2024

Modern Stochastics: Theory and Applications

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The purpose of this paper is to explore two probability distributions originating from the Kies distribution defined on an arbitrary domain. The first one describes the minimum of several Kies random variables whereas the second one is for their maximum – they are named min- and max-Kies, respectively. The properties of the min-Kies distribution are studied in details, and later some duality arguments are used to examine the max variant. Also the saturations in the Hausdorff sense are investigated. Some numerical experiments are provided.

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Section: Unemployment Insurance Issuesmentioning

confidence: 70%

“…Refs. [1,3,9,10] use a power transformation to define new families. Some composite distributions are proposed in [3], see also [1,4,16,20].…”

Section: Introductionmentioning

confidence: 99%

On min- and max-Kies families: distributional properties and saturation in Hausdorff sense

Zaevski,

Kyurkchiev

2024

Modern Stochastics: Theory and Applications

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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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“…is section discusses how to estimate the ExRK model parameters using several classical estimation approaches by maximization or minimization of the considered function. For more details, see [15][16][17][18][19].…”

Section: Estimation Methodsmentioning

confidence: 99%

A Flexible Extension of Reduced Kies Distribution: Properties, Inference, and Applications in Biology

et al. 2022

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The extended reduced Kies distribution (ExRKD), which is an asymmetric flexible extension of the reduced Kies distribution, is the subject of this research. Some of its most basic mathematical properties are deduced from its formal definitions. We computed the ExRKD parameters using eight well-known methods. A full simulation analysis was done that allows the study of these estimators’ asymptotic behavior. The efficiency and applicability of the ExRKD are investigated via the modeling of COVID-19 and milk data sets, which demonstrates that the ExRKD delivers a better match to the data sets when compared to competing models.

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Power-Modified Kies-Exponential Distribution: Properties, Classical and Bayesian Inference with an Application to Engineering Data

Cited by 23 publications

References 20 publications

On min- and max-Kies families: distributional properties and saturation in Hausdorff sense

On min- and max-Kies families: distributional properties and saturation in Hausdorff sense

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

A Flexible Extension of Reduced Kies Distribution: Properties, Inference, and Applications in Biology

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