New Weibull X-Lindley distribution: Structure and Properties

Abdullah Rabah  Abbar; Ali Talib Mohammed; Umar  Yusuf Madaki

doi:10.30526/39.4.4345

Authors

Abdullah Rabah Abbar Department of Mathematics, College of Education for Pure Science (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq https://orcid.org/0009-0000-0510-6400
Ali Talib Mohammed Department of Mathematics, College of Education for Pure Science (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq https://orcid.org/0009-0000-0510-6400
Umar Yusuf Madaki Department of Mathematics and Statistics, Faculty of Science, Yobe State University, Damaturu, Nigeria https://orcid.org/0000-0002-2242-9698

DOI:

https://doi.org/10.30526/39.4.4345

Keywords:

Weibull X-Lindley, X-Lindley, Characteristic Function, Mean time to failure, Quantile function

Abstract

This paper aims to introduce a novel univariate probability distribution called the Weibull X-Lindley distribution (W-XLD), designed to be more flexible in modeling data with different patterns. The core idea behind this distribution arose to address some of the limitations of traditional distributions by introducing a form factor to increase flexibility to the proposed distributions. The technique used to construct W-XLD relies on multiplying the survival functions of the X-Lindley and Weibull distributions to find the W-XLD survival function. Based on this, the statistical functions of W-XLD were defined, including the cumulative distribution function (cdf), the probability density function (pdf), and the risk function. The shapes of the distribution functions for various conditional data and parameter values were discussed. The distribution parameters are two: the shape parameter (β) and the scale parameter (ϑ). The properties of the density and risk functions at the boundaries of the random variable domain were examined, based on finding their boundary values. Furthermore, the basic and statistical characteristics were extracted, analyzed, given, and studied., including pattern, moments, kurtosis, skewness, variance, generated moments, quantiles, mean time to failure, and segmentation

Author Biographies

Abdullah Rabah Abbar , Department of Mathematics, College of Education for Pure Science (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq

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Ali Talib Mohammed, Department of Mathematics, College of Education for Pure Science (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq

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Umar Yusuf Madaki, Department of Mathematics and Statistics, Faculty of Science, Yobe State University, Damaturu, Nigeria

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