Probability-generating function

About: Probability-generating function is a research topic. Over the lifetime, 752 publications have been published within this topic receiving 9361 citations.

A New Weighted Information Generating Function for Discrete Probability Distributions

Abstract: The object of this paper is to introduce a new weighted information generating function whose derivative at point 1 gives some well known measures of information. Some properties and particular cases of the proposed generating function have also been studied.

Delay in a 2-State Discrete-Time Queue with Stochastic State-Period Lengths and State-Dependent Server Availability and Arrivals

Abstract: In this paper, we consider a discrete-time multiserver queueing system with correlation in the arrival process and in the server availability. Specifically, we are interested in the delay characteristics. The system is assumed to be in one of two different system states, and each state is characterized by its own distributions for the number of arrivals and the number of available servers in a slot. Within a state, these numbers are independent and identically distributed random variables. State changes can only occur at slot boundaries and mark the beginnings and ends of state periods. Each state has its own distribution for its period lengths, expressed in the number of slots. The stochastic process that describes the state changes introduces correlation to the system, e.g., long periods with low arrival intensity can be alternated by short periods with high arrival intensity. Using probability generating functions and the theory of the dominant singularity, we find the tail probabilities of the delay.

On the limiting distribution of the maximum with random sample size of regular variation function

Abstract: Let X 1 , X 2 , … be i.i.d. sequence and ƒ(x) be a regular variation function with index r. Let N(n) be a positive integer valued random variable and equation in probability, where η is a positive random variable. When some conditions are satisfied, the asymptotic distribution of M ƒ(N(n)) is derived.

Functions of Random Variables

Abstract: For the simple events of a sample space, we can define more than one random variable function; in fact, we can define infinitely many random variable functions, i.e., random variables, and for a variety number of random variables, we can define joint probability mass and cumulative distribution function. In this chapter, we provide information about joint probability mass functions of more than one random variable, functions of random variables, conditional probability mass functions, and corresponding mean and variance calculations. Solved examples are utilized to explain the subjects in a clear manner.

Statistical characterization of the output of nonlinear power-cubic detection unit for ultrashort light pulse communication in the presence of Gaussian noise

Abstract: In this paper, an accurate model for the probability density function (pdf) of the random decision variable Y in an ultrafast digital lightwave communication system, utilizing power-cubic all-optical nonlinear preprocessor is presented. The proposed model can replace the prevalent Gaussian approximation, as the accuracy of the latter is discredited by Monte-Carlo simulation. The Log-Pearson type-3 probability density function (LP3 pdf) is shown to appropriately represents the random decision variable Y. Three characteristic parameters of the LP3 pdf are also obtained through the three moments of the decision variable Y. Finally, the system error probability is revisited using the obtained LP3 pdf of the decision variable, the result of which is in excellent consistency with rigorous Monte-Carlo simulation.