A New Modified Alpha Power Weibull Distribution: Properties, Parameter Estimation and Application

A new lifetime distribution called alpha power modified Weibull (APMW) distribution based on the alpha power transformation method has been studied. Various statistical properties of the newly developed distribution including quantiles, moments, stress-strength parameter, Bonferroni and Lorentz curve, residual and reversed residual lifetime function, stress-strength parameter, entropy and order statistics have been obtained. Percentage points of the APMW distribution for different values of the parameters have been obtained. The method of maximum likelihood estimation (MLE) has been used for estimating the parameters. A simulation study has been performed to evaluate the behaviour of the MLEs in terms of the sample size n and revealed that as the value of the sample size increases the value of the mean square error decreases showing the reliability of the estimators. The efficiency and flexibility of the new distribution are illustrated by analysing three real-life data sets. In each case, the APMW distribution provides a better fit indicating that the APMW distribution is a justifiable choice for fitting the considered data sets.