The article substantiates the relevance of processing statistical data on natural processes that lead to emergencies and negatively affect the environmental situation. Informationis provided on determining the consistency of samples of random variables of parameters of such processes according to known distribution laws using the Pearson and Kolmogorov criteria, as wellas the consistency of estimates and coefficients of variation, asymmetry and kurtosis of a sampleof random variables and the distribution law. It is shown that the β-distribution of the 1-st kind canbe accepted as a universal approximating law and analytical expressions can be derived to find its parameters. Using the examples of statistics on the average annual water consumption in the riverand the energy parameters of seismic events, analytical expressions are derived for the corresponding probability densities of β-distributions of the 1-st kind. The probabilities of the occurrence of negative events are estimated based on the thresholds of the average annual water consumption and the energy parameter of seismic events, respectively. The conclusion is made about the possibility of effective use of the β-distribution of the 1-st kind for the analysis of statistical data of a wide class of natural and man-made processes.