Theory and application of the power Ailamujia distribution

Statistical modeling is constantly in demand for simple and flexible probability distributions. We are helping to meet this demand by proposing a new candidate extending the standard Ailamujia distribution, called the power Ailamujia distribution. The idea is to extend the adaptability of the  Ailamujia distribution  through the use of the power transform, introducing a new shape parameter in its definition. In particular, the new parameter is able to produce original non-monotonic shapes for the main functions that are desirable for data fitting  purposes. Its interest is also shown through results about stochastic orders, quantile function, moments (raw, incomplete and probability weighted), stress-strength parameter and Tsallis entropy. New classes of distributions based on the power Ailamujia distribution are also presented. Then, we investigate the  corresponding statistical model to analyze two kinds of data:  complete data and data in presence of censorship.  In particular, a goodness-of-fit statistical test allowing the processing of right-censored data is developed. The potential of the new model is demonstrated by its application  to four data sets, two being related to the Covid-19 pandemic.