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Probabilistic models for sequence of the independent tests with three outcomes


I.G. Karpov, V.D. Popelo, D.K. Proskurin

Important component of technologies of creation of technical systems of different function, the pilot researches conducted at various stages of life cycle of these systems, directed on obtaining quantitative data on the size of indicators of quality (efficiency) of their functioning both continuous, and discrete character are. Data on continuous sizes obtain during measurements, and about discrete in the course of calculation. Experiments with calculation favorable and failures of various events usually use for definition of probabilistic indicators of quality of technical systems, and mathematical model of such experiments is the scheme of tests of Bernoulli Schema of tests of Bernoulli leads to several extremely important probabilistic models: to binomial distribution, Poisson's distribution, negative binomial distribution, geometrical distribution. Despite extremely wide scope of the scheme of tests of Bernoulli in experiments according to the estimates of the phenomena, this scheme doesn't settle all variety of possible situations at definition of probabilistic indicators of quality (efficiency) of technical systems. In a particular, not always it is possible to reduce results of independent tests by two opposite outcomes. Such situation arises, for example, if the decision on accessory of some outcomes of tests to sets of «successes» or «failures» can't be accepted unambiguously. The work purpose – to develop probabilistic models for sequence of independent tests with three outcomes. It is established that probabilistic models for sequence of independent tests with three outcomes can be presented by group of one-dimensional distributions of trinomialny type. Special cases of these Distributions at zero probability of one of outcomes of tests are probabilistic models, characteristic for Bernoulli's scheme. Expressions for calculation of the main numerical characteristics of the constructed three-nominally distributions for sequence of independent tests with three outcomes are received.

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