Different Estimation Methods for Type I Half-Logistic Topp–Leone Distribution

Ramadan A. ZeinEldin, Christophe Chesneau, Farrukh Jamal and Mohammed Elgarhy
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Ramadan A. ZeinEldin: Deanship of Scientific Research, King AbdulAziz University, Jeddah 21442, Saudi Arabia
Christophe Chesneau: Department of Mathematics, Université de Caen, LMNO, Campus II, Science 3, Caen 14032, France
Farrukh Jamal: Department of Statistics, Govt. S.A Postgraduate College Dera Nawab Sahib, Bahawalpur, Punjab 63100, Pakistan
Mohammed Elgarhy: Valley High Institute for Management Finance and Information Systems, Obour, Qaliubia 11828, Egypt

Mathematics, 2019, vol. 7, issue 10, 1-23

Abstract: In this study, we propose a new flexible two-parameter continuous distribution with support on the unit interval. It can be identified as a special member of the so-called type I half-logistic-G family of distributions, defined with the Topp–Leone distribution as baseline. Among its features, the corresponding probability density function can be left skewed, right-skewed, approximately symmetric, J-shaped, as well as reverse J-shaped, making it suitable for modeling a wide variety of data sets. It thus provides an alternative to the so-called beta and Kumaraswamy distributions. The mathematical properties of the new distribution are determined, deriving the asymptotes, shapes, quantile function, skewness, kurtosis, some power series expansions, ordinary moments, incomplete moments, moment-generating function, stress strength parameter, and order statistics. Then, a statistical treatment of the related model is proposed. The estimation of the unknown parameters is performed by a simulation study exploring seven methods, all described in detail. Two practical data sets are analyzed, showing the usefulness of the new proposed model.

Keywords: type I half-logistic distribution; Topp–Leone distribution; estimation methods; data analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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