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A New Extension of Lomax Distribution: Properties, Inference, Simulation, and Applications |
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PP: 1511-1544 |
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doi:10.18576/amis/200606
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Author(s) |
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Hazar A. Khogeer,
Mustafa Kamal,
Yousef Alharbi,
Eslam Hussam,
Mohamed Said Mohamed,
Ahmad Abubakar Suleiman,
Maryam Ibrahim Habadi,
Mohammed Elgarhy,
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Abstract |
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| Lifetime data arising in reliability engineering, survival analysis and risk modeling are often skewed and heavy-tailed, and their tails are not always well described by classical lifetime models. We propose a two-parameter model, the Entropy- Transformed Lomax (ETLx) distribution, obtained by applying an entropy-based transformation to the Lomax distribution. Most Lomax generalizations gain flexibility by adding shape parameters; the ETLx model keeps the two original parameters and can still accommodate positively skewed, heavy-tailed data. We derive explicit expressions for the density, distribution, survival and hazard rate functions, the quantile function (written with the Lambert W function), the ordinary and incomplete moments, the moment generating function, skewness, kurtosis, and the Re ́nyi and Tsallis entropies. The parameters are estimated by maximum likelihood, and a Monte Carlo study is used to check how the estimators behave in finite samples. Three lifetime datasets are then fitted with the ETLx model and with the Lomax, Weibull, Gamma, Lognormal and Exponential distributions. The fits are compared through the log-likelihood, the Akaike (AIC), Bayesian (BIC), Hannan–Quinn (HQIC) and consistent Akaike (CAIC) information criteria, and the Kolmogorov– Smirnov (KS), Crame ́r–von Mises (CVM) and Anderson–Darling (AD) statistics. For all three datasets the ETLx model gave the smallest information criteria and the best goodness-of-fit values, which suggests that it is a sensible choice for heavy-tailed lifetime data. |
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