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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.


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Journal ArticleDOI
TL;DR: In this paper, the Galton-Watson branching process is considered and estimators for the offspring probabilities and probability generating functions and for the extinction probability are defined for the non-subcritical case and the subcritical case.
Abstract: Estimators for the offspring probabilities and probability generating functions and for the extinction probability are defined for the Galton-Watson branching process. These estimators are shown to be conditionally consistent and asymptotically normal in the non-subcritical case and to lack these properties in the subcritical case. Corresponding questions are considered when immigration is permitted.

22 citations

Journal ArticleDOI
TL;DR: Two important substantive conclusions drawn from the Monte Carlo experiments were that efforts should be made to collect quantitative information on the probability of infection per sexual contact as a function of duration of infection and the frequency of condom use within and among risk categories in a population.
Abstract: A nonlinear stochastic model of an AIDS epidemic with recruitment of infectives, susceptibles, and AIDS cases into a randomly mixing population of male homosexuals was formulated and studied from a methodological point of view through intensive computer experimentation. Probability generating functions were used to formulate a model for the monthly probability that a susceptible individual becomes infected with HIV, under the assumption that the probability of infection per sexual contact varies as a function of the duration of infection. A method for taking into account the use of condoms to prevent infection with HIV was also introduced. Nonlinear difference equations, resembling deterministic epidemic models, were embedded in the stochastic population process by iterating an initial conditional expectation. Examples of Monte Carlo experiments are presented, illustrating that solutions of these nonlinear difference equations are not always good measures of central tendency for variations in the sample functions of the process. Two important substantive conclusions drawn from the Monte Carlo experiments were that efforts should be made to collect quantitative information on the probability of infection per sexual contact as a function of duration of infection and the frequency of condom use within and among risk categories in a population.

21 citations

DOI
01 Dec 1985
TL;DR: A new metric, termed `recovery distance?
Abstract: A new metric, termed `recovery distance?, is introduced for decision feedback receivsers, and is shown to provide the basis for a simple technique for obtaining bounds on a wide range of error statistics. The error propagation process is modelled using stochastic state transition diagrams with merging of states having the same recovery distance, providing the simplification required to render tractable the derivation of probability generating functions for error random variables of interest. The new technique is illustrated by deriving bounds on error statistics for various signal formats of interest for practical applications.

21 citations

Journal ArticleDOI
TL;DR: In this paper, the authors investigated the problem of finding the distribution of distances between successive occurrences of So and S 0 and S 1 and the waiting time until the rth occurrence of So in multistate Markov dependent trials.
Abstract: In this paper, we investigate sooner and later waiting time problems for patterns So and S 1 in multistate Markov dependent trials. The probability functions and the probability generating functions of the sooner and later waiting time random variables are studied. Further, the probability generating functions of the distributions of distances between successive occurrences of So and between successive occurrences of S 0 and S 1 and of the waiting time until the rth occurrence of So are also given.

21 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20236
202211
20217
202014
201912
20188