Open AccessMarshall-Olkin Lehmann Lomax Distribution: Theory, Statistical Properties, Copulas and Real Data Modeling
Author(s) -
Mohamed Aboraya
Publication year - 2021
Publication title -
pakistan journal of statistics and operation research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.354
H-Index - 15
eISSN - 2220-5810
pISSN - 1816-2711
DOI - 10.18187/pjsor.v17i2.3732
Subject(s) - mathematics , lomax distribution , skewness , gumbel distribution , monotonic function , estimator , copula (linguistics) , statistics , bivariate analysis , kurtosis , maximum likelihood , econometrics , extreme value theory , mathematical analysis
In this work, a new four-parameter lifetime probability distribution called the Marshall-Olkin Lehmann Lomax distribution is defined and studied. The density function of the new distribution "asymmetric right skewed" and "symmetric" and the corresponding hazard rate can be monotonically increasing, increasing-constant, constant, upside down and monotonically decreasing. The coefficient of skewness can be negative and positive. We derive some new bivariate versions via Farlie Gumbel Morgenstern family, modified Farlie Gumbel Morgenstern family, Clayton Copula and Renyi's entropy.The method of maximum likelihood is used to estimate the unknown parameters. Using "biases" and "mean squared errors", a simulation study is performed for assessing the finite behavior of the maximum likelihood estimators.