Ipo Estimation Of Heaviness Of The Distribution Beyond Regularly Varying Tails

We introduce a completely novel method for estimation of the parameter which governs the tail behavior of the cumulative distribution function of the observed random variable. We call it Inverse Probabilities for p-Outside values (IPO) estimation method. We show that this approach is applicable for wider class of distributions than the one with regularly varying tails. We demonstrate that IPO method is a valuable competitor to regularly varying tails based estimation methods. Some of the properties of the estimators are derived. The results are illustrated by a convenient simulation study.