THE DETERMINATION OF DISTRIBUTION PARAMETERS OF ONE-DIMENSIONAL CONTINUOUS RANDOM VARIABLE ACCORDING TO ITS INITIAL CHARACTERISTICS BY FINANCIAL RISKS MODELLING

The conception of direct and inverse problem of random variable modelling is introduced. The direct problem is a problem for getting value of continuous random variable, which is contributed according to the given distribution law, which parameters are known. The inverse problem is a problem for defining the distribution law parameters, which are necessary for modelling of continuous one-dimensional random variable, for which the distribution law, mathematical expectation and dispersion are known. For its solution by known type of distribution it is necessary to find the parameter dependence of simulated distribution on set initial characteristics – ensemble average and standard deviation. The assigned problem is solved in explicit form for the following cases: normal distribution, exponential distribution, Laplace distribution, extreme value minimum distribution, extreme value maximum distribution, double exponential distribution, logistic distribution, gamma distribution, Erlang distribution of n-th order, Rayleigh distribution, Maxwellian distribution, parabolic distribution, Simpson distribution, arc sine distribution, inverse Gaussian distribution , Cauchy distribution, one-parameter distribution of n-dimansional random value, hyperexponential distribution, beta distribution, common- beta distribution, Birnbaum-Sanders distribution.For random variables, which are distributed according to the laws: Erlang second order, beta-distribution of second order, logarithmic normal distribution, it is described the interactive procedure to solve the modelling inverse problem, which realizes theNewton's method for solution of linear equation system. The expressions for elements of matrix solution are received. The solution procedure of assigned task for Weibull and Nakagami distribution is set, which is based on construction of regressive equations, which interpolate the table values to determine links of distribution law parameters and initial characteristics of random variable, which is distributed according to the given law.