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Models of laws of distribution continuous random variables on the basis of exponential distribution

Keywords:

I.G. Karpov – Dr.Sci. (Eng.), the professor of chair of information systems and protection of information, Тambov State Тechnical University G.N. Nurutdinov ― Ph.D. (Eng.), Associate Professor of chair of information systems and protection of information, Тambov State Тechnical University. E-mail:nurutgn@mail.ru


Now in various appendices of probability theory and mathematical statistics along with Gaussian distribution exponential distribution is widely used. The density of distribution of probabilities (PRV) of a difference of two independent random variables having exponential distribution is received. The area of existence of this PRV almost coincides with area of existence of distributions of Pearson and it doesn't include only existence area a beta - distributions. It is offered to call PRV bilateral gamma distribution, and its special case – bilateral exponential distribution. Expressions for the main numerical characteristics of distributions are given, and also limit cases of PRV are considered. It should be noted that PRV, also as well as Gaussian distribution, is infinitely divisible distribution. Thus, the model infinitely divisible laws of distribution of the continuous random variables accepting both positive, and negative values is developed.
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