In this work we focus on the problem of parameter estimation of distribution tails. The problem of tail estimation is central to statistics of extremes of independent observations. The generally accepted approach to estimate the distribution tail in this theory is semi-parametric and based on Pickands-Balkema-de Haan theorem reducing this problem to the problem of estimating the extreme value index. The mentioned approach works well for distributions with power-law tails, that often appears in finance and insurance. However, one cannot distinguish between the distribution tails with exponential rate of decrease using this approach. Moreover, the conditions of Pickands-Balkema-de Haan theorem are not satisfied for the large class of distributions, in particular, distributions with logarithmic tails. Therefore, it becomes necessary to propose the general method of tail estimation not based on the latter theorem such that it can be applied to most distributions used in practice.
