Methods of Calculating of Quantiles of Various Orders

Abstract

The methods of calculation of quantiles of various orders are considered in the work. The procedure for the definition of quantiles on selected theoretical distribution is introduced. It presents an algorithm for determining the distribution function, including the procedure of histograming, the choice of the formula for the empirical distribution function, the determination of the parameter estimates by the method of quantiles with the examples for various practical cases. The technique for the determination of quantiles approximated by the empirical distribution function based on nuclear estimation and interpolation by splines and orthogonal polynomials is presented.