Showing papers on "Probability-generating function published in 1980"

Some Techniques for Solving Recurrences

Abstract: Some techmques for solving recurrences are presented, along with examples of how these recurrences arise in the analysis of algorithms. In addition, probability generating functions are discussed and used to analyze problems in computer science.

Memory as a Property of Probability Distributions

Abstract: The probability law of a positive random variable with finite mean is uniquely determined by the mean residual life (MRL) function. This function is useful as an indicator of aging and similar mechanisms. Memory is defined and several measures of memory are derived from the MRL function. Properties of the MRL function and the hazard function are compared. A class of distributions with convex decreasing MRL function, which forms a proper subset of the class of distributions with increasing hazard function, is defined. It is indicated how representative distributional models can be constructed from data.

A New Look at Convergence of Branching Processes

Abstract: The classical almost sure convergence of the normed supercritical Galton-Watson branching process with finite mean is obtained by a new method which does not involve probability generating functions.

Series expansions of probability generating functions and bounds for the extinction probability of a branching process

Abstract: In the Taylor series expansion about s = 1 of the probability generating function f(s) of a non-negative integer-valued random variable with finite nth factorial moment the remainder term is proportional to another p.g.f. This leads to simple proofs of other power series expansions for p.g.f.'s, including an inversion formula giving the distribution in terms of the moments (when this can be done). Old and new inequalities for the extinction probability of a branching process are established. PROBABILITY GENERATING FUNCTIONS; FACTORIAL MOMENTS; BRANCHING PROCESS EXTINCTION PROBABILITY BOUNDS

Transition probability matrices for correlated random walks

Abstract: For correlated random walks a method of transition probability matrices as an alternative to the much-used methods of probability generating functions and difference equations has been investigated in this paper. To illustrate the use of transition probability matrices for computing the various probabilities for correlated random walks, the transition probability matrices for restricted/unrestricted one-dimensional correlated random walk have been defined and used to obtain some of the probabilities.

Deriving sediment yield probabilities for evaluating conservation practices.

Abstract: PROBABILITY distributions of annual sediment yield are derived for both conventional and minimum tillage of watershed cropland. For the derivation, a recursive technique derived from probability generating functions is used to couple a bivariate rainfall model and a stochastic watershed state model to a deterministic model of the sediment yield process. The bivariate rain-fall model consists of a Weibull PDF for rainfall event duration and a log-normal PDF for event depth, given duration; the stochastic state model is a probability mass function for antecedent rainfall class; the deterministic model is composed of the Williams sediment-yield model and SCS techniques for computing direct runoff volume and peak runoff rate.