Showing papers on "Probability-generating function published in 1968"

Infinite dams with inputs forming a Markov chain

Abstract: This paper considers a finite dam fed by inputs forming a Markov chain. Relations for the probability of first emptiness before overflow and with overflow are obtained and their probability generating functions are derived; expressions are obtained in the case of a three state transition probability matrix. An equation for the probability that the dam ever dries up before overflow is derived and it is shown that the ratio of these probabilities is independent of the size of the dam. A time dependent formula for the probability distribution of the dam content is also obtained.

Survival probabilities f new inversions in large populations.

Abstract: The survival process of newly induced inversions in infinite populations was investigated. The system was formulated as a branching process of inversion descendants in discrete time, and the method of probability generating functions was applied. The fitness value of inversions was a time-dependent variable, and the process was represented as a time-heterogeneous branching process. In order to deal with such a heterogeneous process, an approximate method was developed on the basis of the continuous time approximation. Using this method, approximate solutions of ultimate survival probabilities were obtained for relatively simple genetic situations. It was also shown that the extinction of descendants of any new inversion is certain unless an inversion is provided with a unique mechanism by which it can permanently maintain some selective superiority.

A review of the collective theory of risk

Abstract: Let the random variable ξ be distributed with distribution function G(ξ) of the continuous, discontinuous or mixed type, and the random variables x ξ be distributed with the distribution functions V ξ(x) with the corresponding characteristic functions , η being a real variable, and i the imaginary unit, and with the generating functions defined by ψξ(− i log z). If the range of x is restricted to the right semi-plane the lower limit of the integral in the definition of ψξ(η) can be replaced by zero.

An Additional Special Channel, Limited Space Queuing Problem with Service in Batches of Variable Size

Abstract: This paper studies the transient behavior of a first-come-first-served queuing problem with service in batches of variable size, Poisson input, and exponential service time distribution. Further, when the queue length increases to N, a fixed pre-assigned positive number, a special service channel capable of serving a group of N units and possessing exponential service time distribution is made available and is canceled at the termination of service if the queue length becomes less than N. Also a limited waiting space K is assumed for the waiting line. The Laplace transforms of various probability generating functions are obtained and the corresponding results for the steady state are derived. Finally, some particular cases are discussed.

Generation of random digital numbers with specified probability distributions

Abstract: Current interest in digital simulation models has given rise to the need to produce random digital numbers. Several methods of generating pseudo-random sequences of digital numbers are discussed. These methods are used as a basis for generating truly random digital numbers whose probability of occurrence can be set by programming a simple patch-board.