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Abstract

A new G family of probability distributions called the type I quasi Lambert family is defined and applied for modeling real lifetime data. Some new bivariate type G families using "Farlie-Gumbel-Morgenstern copula", "modified Farlie-Gumbel-Morgenstern copula", "Clayton copula" and "Renyi's entropy copula" are derived. Three characterizations of the new family are presented. Some of its statistical properties are derived and studied. The maximum likelihood estimation, maximum product spacing estimation, least squares estimation, Anderson-Darling estimation and Cramer-von Mises estimation methods are used for estimating the unknown parameters. Graphical assessments under the five different estimation methods are introduced. Based on these assessments, all estimation methods perform well. Finally, an application to illustrate the importance and flexibility of the new family is proposed.

Keywords

Characterizations Copula Maximum Product Spacing Maximum Likelihood Anderson-Darling Estimation

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How to Cite
Hamedani, G. G., Korkmaz, M. C., Butt, N. S., & Yousof, H. M. (2021). The Type I Quasi Lambert Family . Pakistan Journal of Statistics and Operation Research, 17(3), 545-558. https://doi.org/10.18187/pjsor.v17i3.3562
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