IPO and IPO-NM estimators in exponentiated Fréchet case.

In 2003 Nadarajah and Kotz investigated Exponentiated-Fréchet distribution. They showed that its cumulative distribu- tion function has regularly varying right tail. An interesting fact about this distribution is that its index of regular variation depends on two parameters. In 2019 Jordanova defined and investigated the main properties of p-outside values and showed that they do not depend on the center and the scale parameter of the considered distribution. Therefore, they are appropriate for estimation of the parameters which govern the tail-behavior of the c.d.f. IPO and MN-IPO estimators were introduced by Jordanova and Stehlik in 2019 in the general case. Here we compute probabilities for right p-outside values in Exponentiated-Fréchet case. Then, we express the unknown parameters via the empirical relative frequencies of these p-outside values. We observe that the corresponding system of equations has no explicit solution, therefore, we solve it by using new appropriate numerical methods. The last solutions are the so called IPO-NM estimators. If we use, as an auxiliary characteristic the empirical p-fences, we show that the corresponding system of equations has an easier solution and these are the IPO estimators. The properties of IPO and IPO-NM estimator are discussed. The rates of convergences of the last are visualized via a simulation study. The corresponding distribution sensitive estimators of the quantiles outside the range of the data are obtained. The paper finishes with some conclusive remarks where new open problems are posed. [ABSTRACT FROM AUTHOR]