textit{A priori} Frechet and scaled inverse chi distribution in Bayesian balance models

This article continues a series of authors' works in the field of modeling queuing systems using the Bayesian approach. The problem's statement is extended to a wider class of applied research — the study of the balance index of factors affecting the functioning of the system. It is assumed that the model parameters are divided into two classes, one of which includes factors that have a positive impact on the functioning of a complex aggregate and the other includes those that interferes with the functioning. The effectiveness of the system under study, of course, depends on the ratio of positive and negative factors, called the balance index. In the framework of the Bayesian approach, it is assumed that the factors are random variables with known a priori distributions. In a wide range of applied problems, it is reasonable to use gamma-type distributions. In this paper, the mixtures of particular generalized gamma distribution cases — the Frechet distribution and the scaled inverse chi distribution — are considered.