COMPARISON OF SOME METHODS FOR ASSESSING THE WEIGHT OF TAILS IN IDENTIFICATION OF THE DISTRIBUTION LAW
The article deals with the problem of identification of the distribution law. It is shown that the distribution law is an exhaustive characteristic of a random data array. In this case, in the absence of a priori knowledge of the distribution law, the processing of the data array available to the researcher presents certain difficulties, the solution of which is possible by identifying the distribution law. The article provides a brief overview of the main methods for identifying distribution laws, while it is noted that characteristics calculated directly from the original data array can help in identifying the distribution law. One of these characteristics is the severity of the tail of the probability distribution. It is shown that there is no single universal method for assessing the severity of the tail, and, in particular, for the purpose of identifying the distribution law. The article discusses the Hill assessment method, but it is shown that the method itself is quite laborious when performing calculations. Based on this, a new relationship method is proposed based on the ratio of the main and tail parts of the distribution. At the same time, the question of determining the boundaries of the main and tail parts of the distribution according to the original data array is solved. Five different distribution laws were selected as the basis for the study, differing in the weight of the tail. At the same time, all the laws were selected taking into account the equality of the remaining parameters, in particular, each of the selected distribution laws is symmetric about the center. The proposed new method of relations is compared with the widely known and applied in practice Hill’s estimate. It is proved that in the question of identifying the distribution law, Hill’s estimate gives, in general, a positive result. At the same time, it was shown that the most optimal is the application of the method of relations with a level of 5 %.