The Alpha Power Modified Weibull-Geometric Distribution: A Comprehensive Mathematical Framework with Simulation, Goodness-of-fit Analysis and Informed Decision making using Real Life Data

A new lifetime distribution by compounding the Alpha Power Modified Weibull distribution, named Alpha Power Modified Weibull-Geometric distribution is introduced and discussed.The compounding of the distribution is motivated from the failure time of the system with series structure, where only the minimum lifetime value is considered. Various Statistical properties of the proposed distribution are investigated. Maximum likelihoodestimation method is used to estimate the model parameter. To assess the performance of the proposed method, monte carlo simulation study is conducted using various choices of effective sample size and parameter value. Finally, to illustrate the capability and flexibility of the proposed distribution, three real life data sets are considered and showed that the proposed distribution is more compatible by comparing with other competing lifetime distributions.