Generalized Weibull-Lindley (GWL) distribution in modeling lifetime data (Q827174)

Summary: 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.