The article explores how nonparametric goodness-of-fit tests can be affected when estimating distribution parameters from the same sample in composite hypotheses testing. The researchers investigated the statistic distribution models for these tests using maximum likelihood estimates for certain probability distribution laws. Through statistical simulation, they constructed empirical statistic distributions and approximated them with analytical models. The study provides more precise results and tables of percentage points for these tests, shedding light on the impact of various factors on the conditional distribution law of the statistic.