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Statistical Inference of the Half-Logistic Inverse Rayleigh Distribution

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Statistics Department, Faculty of Science, King AbdulAziz University, Jeddah 21577, Saudi Arabia
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Statistics Department, Faculty of Science for Girls, University of Jeddah, Jeddah 21577, Saudi Arabia
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Valley High Institute for Management Finance and Information Systems, Obour, Qaliubia 11828, Egypt
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Department of Statistics, Government Postgraduate College Der Nawab Bahawalpur, Punjab 63351, Pakistan
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Department of Mathematics, LMNO, Campus II, Science 3, Université de Caen, 14032 Caen, France
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Author to whom correspondence should be addressed.
Entropy 2020, 22(4), 449; https://doi.org/10.3390/e22040449
Received: 28 March 2020 / Revised: 12 April 2020 / Accepted: 13 April 2020 / Published: 15 April 2020
The inverse Rayleigh distribution finds applications in many lifetime studies, but has not enough overall flexibility to model lifetime phenomena where moderately right-skewed or near symmetrical data are observed. This paper proposes a solution by introducing a new two-parameter extension of this distribution through the use of the half-logistic transformation. The first contribution is theoretical: we provide a comprehensive account of its mathematical properties, specifically stochastic ordering results, a general linear representation for the exponentiated probability density function, raw/inverted moments, incomplete moments, skewness, kurtosis, and entropy measures. Evidences show that the related model can accommodate the treatment of lifetime data with different right-skewed features, so far beyond the possibility of the former inverse Rayleigh model. We illustrate this aspect by exploring the statistical inference of the new model. Five classical different methods for the estimation of the model parameters are employed, with a simulation study comparing the numerical behavior of the different estimates. The estimation of entropy measures is also discussed numerically. Finally, two practical data sets are used as application to attest of the usefulness of the new model, with favorable goodness-of-fit results in comparison to three recent extended inverse Rayleigh models. View Full-Text
Keywords: inverse Rayleigh distribution; half-logistic transformation; moments; entropy; statistical inference; real data analysis inverse Rayleigh distribution; half-logistic transformation; moments; entropy; statistical inference; real data analysis
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Almarashi, A.M.; Badr, M.M.; Elgarhy, M.; Jamal, F.; Chesneau, C. Statistical Inference of the Half-Logistic Inverse Rayleigh Distribution. Entropy 2020, 22, 449.

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