Comparison of Models of Positively Defined Random Variables

The present study compares the following models of positively defined random variables from a class of probability distributions with a coefficient of variation greater than 1: lognormal, gamma distributions, distribution of Weibull-Gnedenko, hyperexponential distribution of a special kind. The latter has physical visibility, commonality and simplicity. It is well studied and often applied to simplify the modeling of various complex systems. To investigate the properties of the distributions of random variables scatterplots (approach by V. I. Khimenko) are applied. They are simple and illustrative tools. The statistical criteria considered in this paper are clear and understandable for engineers. They reflect such important characteristics of the random flow as the correlation of events, the number and probability of random values exceeding a given level. In general, the analysis allows to conclude that modeling of a positively defined random variable by a two-parameter hyperexponential distribution of a special kind is possible. According to the results obtained, the difference between hyperexponential and the other distributions considered depends on the variation coefficient. As it increases, the approximation properties of hyperexponential distribution deteriorate. Characteristic differences between scatterplots are analyzed for the distributions considered. These are: different random value ranges and degree of concentration in the area of small values. The identified features will help to develop criteria of choosing the random value model and identify the risk of hyperexponential approximation (because of the need to take into account rare but big deviations of random variables).