Abstract
In this manuscript, we have derived a new lifetime distribution named generalized Weibull–Lindley (GWL) distribution based on the T-X family of distribution specifically the generalized Weibull-X family of distribution. We derived and investigated the shapes of its probability density function (pdf), hazard rate function, and survival function. Some statistical properties such as quantile function, mode, median, order statistics, Shannon entropy, Galton skewness, and Moors kurtosis have been derived. Parameter estimation was done through maximum likelihood estimation (MLE) method. Monte Carlo simulation was conducted to check the performance of the parameter estimates. For the inference purpose, two real-life datasets were applied and generalized Weibull–Lindley (GWL) distribution appeared to be superior over its competitors including Lindley distribution, Akash distribution, new Weibull-F distribution, Weibull–Lindley (WL) distribution, and two-parameter Lindley (TPL) distribution.
Highlights
For the past few decades, generation of new distributions has been motivated by the need of fitting complex lifetime data generated from different fields such as engineering, biological and medical sciences, and geology
E rest of the manuscript follows the following order: in the subsequent section, we will give the general form of Weibull-X family of distribution due to Alzaatreh et al [8] and use one-parameter Lindley distribution [9]
Like in many generalized families of distributions, moments of generalized Weibull–Lindley (GWL) is quite complicated to obtain since it involves the expansion of the pdf
Summary
Received 22 May 2020; Revised 1 July 2020; Accepted 22 July 2020; Published 31 August 2020. In this manuscript, we have derived a new lifetime distribution named generalized Weibull–Lindley (GWL) distribution based on the T-X family of distribution the generalized Weibull-X family of distribution. We derived and investigated the shapes of its probability density function (pdf ), hazard rate function, and survival function. Some statistical properties such as quantile function, mode, median, order statistics, Shannon entropy, Galton skewness, and Moors kurtosis have been derived.
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