Ermolaeva

In this paper we consider two etimations of the unknown parameter in the Lehmann-Cox power-law model. These estimates are obtained by minimization of two different functionals: Kolmogorov-Smirnov and Savage ones. The type of these functionals was obtained by using non-parametric statistics proposed by authors in their previous articles. We demonstrated the advantage of one statistics over the other by use of the methods of statistical modeling when the Lehmann-Cox power-law model is valid. It was proposed using a correction coefficient calculated with Monte Carlo method to eliminate bias of estimates for small sample sizes.