Method of Probability Distribution Fitting for Statistical Data with Small Sample Size

Abstract

The paper deals with a new approach for probability distribution fitting for empirical data with small sample size. The proposed method includes three steps: 1) outliers detection and correction; 2) transformation basis calculation; 3) basis function optimization. For the possibility of asymmetric distributions approximation, a piecewise linear basis function is used. During basis function optimization, the dependence of squared deviations sum on switching point abscissa is calculated. The mathematical formula for this dependence can be obtained by quadratic approximation according to the least squares method. The optimum of switching point abscissa coincides with minimum of obtained parabola. Method of probability distribution fitting for statistical data with small sample size is illustrated on the real empirical data example. For this example the best probability distribution fitting corresponds to the case of optimized piecewise linear basis function.