Quadratic Transmuted Modified Size-Biased Lehmann Type-II Distribution

Authors

M. Ibrahem, Department of Basic Sciences, Faculty of Computer and Information Sciences, Ain Shams University, Abbassia, Cairo, EgyptFollow
M. M. Nassar, Department of Mathematics, Faculty of Science, Ain Shams University, Abbassia, Cairo, EgyptFollow
S. S. Radwan, Department of Mathematics, Faculty of Science Girls section, AlAzhar University, Cairo, EgyptFollow
A. Elmasry, Department of Mathematics, Faculty of Science, Ain Shams University, Abbassia, Cairo, EgyptFollow

Author Country (or Countries)

Egypt

Abstract

In this paper, a two-parameter generalization of Modified Size-Biased Lehmann Type-II distribution is obtained, with the purpose of obtaining a more flexible model relative to the behaviour of hazard rate functions. Various statistical properties of this distribution including the density, hazard rate functions, quantile function, mode, moments, incomplete moments, moment generating functions, Lorenz, Bonferroni and Zenga curves, Rényi entropy and distribution of 𝑟# order statistics have been derived. The method of maximum likelihood estimation has been used to estimate the parameters of the Quadratic Transmuted-Modified Size-Biased Lehmann Type-II distribution and its performance is discussed by following a simulation study. Real data sets are presented to demonstrate the effectiveness of the new model.

Digital Object Identifier (DOI)

http://dx.doi.org/10.18576/jsap/12S104

Recommended Citation

Ibrahem, M.; M. Nassar, M.; S. Radwan, S.; and Elmasry, A. (2023) "Quadratic Transmuted Modified Size-Biased Lehmann Type-II Distribution," Journal of Statistics Applications & Probability: Vol. 12: Iss. 4, Article 4.
DOI: http://dx.doi.org/10.18576/jsap/12S104
Available at: https://digitalcommons.aaru.edu.jo/jsap/vol12/iss4/4