An Extension of Three-Parameter Gamma Weibull Distribution: Properties, Estimation and Applications

This paper introduces a new four-parameter weighted distribution called the weighted gamma Weibull distribution. This new distribution is introduced by applying the weighted version to the baseline three-parameter gamma Weibull distribution. The probability density, cumulative distribution, reliability, and hazard rate functions of the new model are provided. The new model contains some lifetime distributions as special cases, including the gamma-Weibull, Weibull, gamma, weighted Weibull, Rayleigh, and exponential distributions, among others. Some statistical properties of the new model are discussed as moments, moment generating function, incomplete moments, inequality measures, entropy measures, and order statistics. The model parameters are estimated by maximum likelihood and least squares methods. Simulation results to assess the performance of the maximum likelihood and least square estimations are discussed at different values of parameters. In addition, two real data sets are fitted to examine the capability of the proposed model and compare it with some other well-known models.