Methods for solving the problem of non-parametric testing of Lehmann's hypotheses when testing parallel systems
The article considers the problem of testing the Lehmann power hypothesis for two censored samples. The Kolmogorov - Smirnov type criterion based on a comparison of the Kaplan - Meier type estimates of the distribution functions for each censored sample is developed to test the power hypothesis. A method for calculating the exact statistics distributions is described on the basis of the model of particle random walk over an integer lattice. The probability values are calculated for a wide range of possible sample sizes. The convergence of this statistics distribution to the standard Kolmogorov - Smirnov distribution is proved provided that the hypothesis being tested is valid. The properties of a power parameter estimate obtained by minimizing statistics are investigated by statistical modeling methods.