On a Numerical Estimation Method with the Given Accuracy of the Quantile Criterion in the Case of a Piece-Linear Loss Function and Gaussian Probability Density

Abstract

The solution of many practical problems leads to the calculation of the values of probabilistic criteria, among which the most common ones are the quantile and probability functionals. It is known that, under fairly general assumptions, methods suitable for solving problems of finding the values of a probabilistic criterion can be used to solve the problem of quantile analysis. The proposed method for solving the problem of quantile analysis is based on the use of the method of numerical multidimensional integration described in the previous works of the author. One of the important properties of this integration method is universality (when using it, we can set an arbitrary number of variables n and an arbitrary number of linear constraints r). The only limitation is the case of the possible unacceptably long solution time. Thus, the indicated universality is transferred to the solution of the considered problem of quantile analysis.