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On the Marei Distribution: A Novel One-Parameter Model with Applications |
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PP: 1407-1426 |
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doi:10.18576/amis/200602
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Author(s) |
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Ghareeb A. Marei,
Doaa Basalamah,
Said G. Nassr,
Ahmed W. Shawki,
Mohammed Elgarhy,
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Abstract |
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| This paper proposes a one-parameter continuous distribution on the positive half-line, named the Marei distribution, obtained by mapping a symmetric beta random variable U with both shape parameters equal to (θ + 1)/2 through the transformation X = pU/(1−U), θ > −1. The objective is a single-parameter model with a power-law right tail and closed-form properties. The density
is decreasing for θ ≤ 0 and unimodal for θ > 0, and its right tail decays as x−(θ+2). Closed-form expressions are derived for the cumulative distribution, survival, hazard rate and quantile functions, raw and incomplete moments, Lorenz and Bonferroni curves, Shannon, Re ́nyi and Tsallis entropies, order statistics, the extreme-value limit and the Fisher information. Every member of the family
hasunitmedianandsatisfiesthereciprocalsymmetryX=d 1/X.Thehazardrateisstrictlydecreasingfor−1<θ≤−1/5andupside- down bathtub shaped for θ > 0, and vanishes at the rate (θ + 1)/x. The model is a regular exponential family, so the maximum likelihood estimator is unique and asymptotically normal for every θ > −1, including parameter values with infinite mean. The parameter is estimated by maximum likelihood with Newton–Raphson iteration and by Bayesian Markov chain Monte Carlo sampling under weak, informative and misspecified priors. A Monte Carlo study covering 25 scenarios confirms consistency, mean squared error decay of order 1/n and nominal interval coverage. On carbon-fibre breaking-stress data and electrical-product failure-time data, the proposed model outperforms fifteen one-parameter competitors in information criteria and goodness-of-fit statistics, performs on par with the half-Cauchy and Lomax distributions, and attains a fit comparable to the two-parameter Weibull and Gamma distributions on the failure-time data with half the number of parameters. The model is recommended for heavy-tailed positive data, and its scale extension is outlined.
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