On a Transmuted Distribution Based on Log-Logistic and Ailamujia Hazard Functions with Application to Lifetime Data

In the past few decades, numerous distributions have been proposedin the literature to model lifetime data. In this paper, the twopopular distributions, Log-Logistic and Ailamujia, were selectedand combined to create a new distribution, namely the Log-LogisticAilamujia distribution, to obtain a distribution that is flexibleto fit data. First, its probability density and cumulativedistribution functions are presented. Then, some distributionalproperties such as survival function, hazard function, weightedmoments, order statistics, and entropy are investigated. Next, theparameters are estimated by the maximum likelihood method, andtheir performance is evaluated via a simulation study with varyingparameter values and sample sizes. Finally, the proposeddistribution is fitted to a real-life data set to examine itsflexibility. The results indicate that the new distributionperforms well. Furthermore, based on the three informationcriteria, the proposed distribution provides a more appropriatemodel than other candidate distributions in terms of goodness offit.