Marshall–Olkin Alpha Power Inverse Exponential Distribution: Properties and Applications

In this paper, we use the method of the Marshall Olkin alpha power transformation to introduce a new generalized Marshall Olkin alpha power inverse exponential (MOAPIE) distribution. Its characterization and statistical properties are obtained, such as reliability, entropy and order statistics. Moreover, the estimation of the MOAPIE parameters is discussed by using maximum likelihood estimation method. Finally, application of the proposed new distribution to a real data representing the survival times in days of guinea pigs injected with different doses of tubercle bacilli 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.