It is introduced in the paper the newly developed optimization method the Stochastic Optimization Algorithm with Probability Vector (PSV). It is related to Stochastic Learning Algorithm with Probability Vector for artificial neural networks. Both algorithms are inspired by stochastic iterated function system SIFS for generating the statistically self similar fractals. The PSV is gradient method...

In this talk, the class of multivariate extended skew normal distributions is introduced. The properties of this class of distributions, such as, the moment generating function, probability density function, conditional probability density functions and independence are discussed. The definition of extended noncentral skew chi-square distribution is given. The necessary and sufficient condition...

Abs t rac t . In the present article we investigate the exact distribution of the waiting time for the r-th non-overlapping appearance of a pair of successes separated by at most k 2 failures (k > 2) in a sequence of independent and identically distributed (rid) Bernoulli trials. Formulae are provided for the probability distribution function, probability generating function and moments and som...

Probability densities that are not uniquely determined by their moments said to be “moment-indeterminate,” or “M-indeterminate.” Determining whether a density is M-indeterminate, how generate an M-indeterminate density, challenging problem with long history. Quantum mechanics inherently probabilistic, yet the way in which probability obtained dramatically different comparison standard theory, i...

Let G be a finite simple group. In this paper we consider the existence of small subsets A with property that, if y∈G is chosen uniformly at random, then high probability y invariably generates together some element A. We prove various results in direction, both positive and negative. As corollary, that two randomly elements group Lie type bounded rank generate away from zero. Our method based ...