In this paper, we briefly review the scheme of counting statistics, in which a probability of the number of monitored or target transitions in a Markov jump process is evaluated. It is generally easy to construct a master equation for the Markov jump process, and the counting statistics enables us to straightforwardly obtain basic equations of the counting statistics from the master equation; t...

In 1986 S. Sattolo introduced a simple algorithm for uniform random generation of cyclic permutations on a fixed number of symbols. Recently, H. Prodinger analysed two important random variables associated with the algorithm, and found their mean and variance. Mahmoud extended Prodinger’s analysis by finding limit laws for the same two random variables. The present article, starting from the de...

A new family of recursive power-series distributions involving the generalized hypergeometric function is proposed. The probability generating and moment generating functions are given; and extensions of the Poisson, geometric, negative binomial, log-series, and generalized Waring distributions are presented as examples.

Consider an infinite tree with random degrees, i.i.d. over the sites, with a prescribed probability distribution with generating function G(s). We consider the following variation of Rényi’s parking problem, alternatively called blocking RSA (random sequential adsorption): at every vertex of the tree a particle (or “car”) arrives with rate one. The particle sticks to the vertex whenever the ver...

In this paper, we present a new method for the study of a discrete random variable whose probability distribution has a finite support. The approach is based on the introduction of a transform of the probability density function, named γ-transform, which better suits the finite nature of the random variable than the traditional probability generating function. In particular, in addition to the ...

Cryptography and simulation of systems require that events of pre-defined probability be generated. This paper presents methods to generate target probability events based on the oblivious transfer protocol and target probabilistic sequences using probability distribution functions.

Although knowing the time of the occurrence of the earthquakes is vital and helpful, unfortunately it is still unpredictable. By the way there is an urgent need to find a method to foresee this catastrophic event. There are a lot of methods for forecasting the time of earthquake occurrence. Another method for predicting that is to know probability density function of time interval between earth...

Stochastic programming is a valuable optimization tool where used when some or all of the design parameters of an optimization problem are defined by stochastic variables rather than by deterministic quantities. Depending on the nature of equations involved in the problem, a stochastic optimization problem is called a stochastic linear or nonlinear programming problem. In this paper,a stochasti...

We construct a class of generalized q-deformed coherent states (Gq-CS) and we introduce generalization the Euler probability distribution for which write down generating function. As application, discuss statistics number operator in these Gq-CS with respect to many parameters.