On some composite Kies families: distributional properties and saturation in Hausdorff sense

The stochastic literature contains several extensions of the exponential distribution which increase its applicability and flexibility. In present article, some properties a new power modified family with an original Kies correction are discussed. This is defined as domain transformed by another distribution. Its probabilistic investigated limitations for saturation in Hausdorff sense derived. Moreover, formula semiclosed form obtained this saturation. Also tail behavior these distributions examined considering three different criteria inspired financial markets, namely, VaR, AVaR, expectile based VaR. Some numerical experiments provided, too.