Inverse Lomax Log-Logistic Distribution with Applications

Abstract

In this article, an extension of the inverse Lomax (IL) distribution with the log-logistic distribution
called iInverse Lomax log-logistic (IL-LL) distribution is considered. Various statistical properties of
IL-LL distribution which include moment generating function, order statistics, moments, and Renyi ´
entropy are derived. The results of a Monte Carlo simulation study to evaluate the performance of
the maximum likelihood parameter estimates of the model are presented. The IL-LL distribution
is applied to three different data sets comprising the proportion of toxicity for chromium in marine
waters; Number of air conditioning faults in jet aircraft; and relief times of patients being given an
analgesic. Using the maximum likelihood estimation method, the analytical criteria, suggests that the
new model fits the data sets better than the existing competitors.