Goodness-of-fit test based on the interval estimation

Abstract

A new goodness-of-fit test constructed with the use of the interval estimation of the probability distribution function is proposed. A comparative analysis of this test with the Kolmogorov test is carried out. It is shown that it is possible to select the correct distribution function and the hypothetical function different from it so that the proposed goodness-of-fit test can have a significantly better performance than the Kolmogorov test. The presented numerical simulation results are in good agreement with the theoretical conclusions.