Topic
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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TL;DR: In this article, the position of the d th occurrence of the maximum value in a sample of n geometric random variables was investigated by means of probability generating functions from which they obtained the asymptotic mean position via Rice's method.
3 citations
TL;DR: By using a rejection algorithm, this work improves the straight-forward method of generating a random permutation until a derangement is obtained and performs an exact average analysis of the algorithm, showing that this approach is rather general and can be used to analyze random generation procedures based on the same rejection technique.
3 citations
TL;DR: The "point of regeneration" method is used to obtain simple sequential equations for determining the complete probability density function for multiple occurrences of events in a Bernoulli sequence.
Abstract: The "point of regeneration" method is used to obtain simple sequential equations for determining the complete probability density function for multiple occurrences of events in a Bernoulli sequence. Both the independent and overlapping classes of recurrent events are included in the general framework of these equations. The equations also lead to the generating function for the probability distribution. This is used to obtain the expected recurrence times for the different classes of recurrent events. A distinction is made between the probability distributions for the occurrence of the k th event at the n th trial and the occurrence of k events in n trials. The latter case is of primary concern. The methods employed and the results obtained have extensive applications in problems in automatic control, communications, and information processing.
3 citations
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TL;DR: Satheesh et al. as discussed by the authors studied generalizations of infinitely divisible and max-infinitely divisible (MID) laws and showed that these generalizations appear as limits of random sums and random maximums respectively.
Abstract: Continuing the study reported in Satheesh (2001),(math.PR/0304499 dated 01 May 2003) and Satheesh (2002)(math.PR/0305030 dated 02May 2003), here we study generalizations of infinitely divisible (ID) and max-infinitely divisible (MID) laws. We show that these generalizations appear as limits of random sums and random maximums respectively. For the random sample size N, we identify a class of probability generating functions. Necessary and sufficient conditions that implies the convergence to an ID (MID) law by the convergence to these generalizations and vise versa are given. The results generalize those on ID and random ID laws studied previously in Satheesh (2001b, 2002) and those on geometric MID laws studies in Rachev and Resnick (1991). We discuss attraction and partial attraction in this generalization of ID and MID laws.
3 citations
TL;DR: In this article, 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.
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.
3 citations