Heavy tailed distributions have a big role in studying risk data sets. Statisticians many cases search and try to find new or relatively statistical models fit sets different fields. This article introduced heavy-tailed model by using alpha power transformation exponentiated log-logistic distribution which called distribution. Its properties were derived mathematically such as moments, moment g...

In this paper, we present a review on the log-logistic distribution and some of its recent generalizations. We cite more than twenty distributions obtained by different generating families univariate continuous or compounding methods distribution. reviewed mathematical properties, including eight functions used to define lifetime distributions. These results were obtain properties generalizatio...

This paper considers a new family of the trimodal skew logistic distributions. Some properties this distribution, including moments, moments generating function, entropy, maximum likelihood estimates parameters and some other properties, are presented. A simulation study is conducted to examine performance parameters. Numerical optimization carried out via two real-life datasets. Results show t...

The parameters of the log-logistic distribution are generally estimated based on classical methods such as maximum likelihood estimation, whereas these usually result in severe biased estimates when data contain outliers. In this paper, we consider several alternative estimators, which not only have closed-form expressions, but also quite robust to a certain level contamination. We investigate ...