Heavy-Tailed Log-Logistic Distribution: Properties, Risk Measures and Applications

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 generating function, quantile entropy, inequality curves order statistics. Five estimation methods the behaviour of proposed parameters was checked randomly generated these methods. Also, some actuarial measures deduced value at risk, tail variance premium. Numerical values for performed proved that has heavier than others compared models. Finally, three real from fields used show how fitting other wells known related