Alpha power inverse Weibull distribution with reliability application

In this paper, we use the method of the alpha power transformation to introduce a new generalized alpha power inverse Weibull (APIW) distribution. Its characterization and statistical properties are obtained, such as reliability, moments, entropy and order statistics. Moreover, the estimation of the APIW parameters is discussed by using maximum likelihood estimation method. Finally, the application of the proposed new distribution to a real data representing the waiting time before customer service in the bank is given and its goodness-of-fit is demonstrated. In addition, comparisons to other models are carried out to illustrate the flexibility of the proposed model.