2010
DOI: 10.1155/2010/675754
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Constant Rate Distributions on Partially Ordered Sets

Abstract: We consider probability distributions with constant rate on partially ordered sets, generalizing distributions in the usual reliability setting ([0, ∞), ≤) that have constant failure rate. In spite of the minimal algebraic structure, there is a surprisingly rich theory, including moment results and results concerning ladder variables and point processes. We concentrate mostly on discrete posets, particularly posets whose graphs are rooted trees. We pose some questions on the existence of constant rate distribu… Show more

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Cited by 2 publications
(4 citation statements)
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“…In probability and statistics, skewness and kurtosis are the third and fourth momen of the distribution (data points) [55]. The Pearson coefficients were computed; fo In probability and statistics, skewness and kurtosis are the third and fourth moment of the distribution (data points) [55].…”
Section: Confocal Microscopymentioning
confidence: 99%
See 1 more Smart Citation
“…In probability and statistics, skewness and kurtosis are the third and fourth momen of the distribution (data points) [55]. The Pearson coefficients were computed; fo In probability and statistics, skewness and kurtosis are the third and fourth moment of the distribution (data points) [55].…”
Section: Confocal Microscopymentioning
confidence: 99%
“…In probability and statistics, skewness and kurtosis are the third and fourth momen of the distribution (data points) [55]. The Pearson coefficients were computed; fo In probability and statistics, skewness and kurtosis are the third and fourth moment of the distribution (data points) [55]. The Pearson coefficients were computed; for skewness the adjusted Fisher-Pearson and for kurtosis the Pearson or excess kurtosis, respectively using Equation (4) [56], where N is the number of data points, x i the data points and x the mean:…”
Section: Confocal Microscopymentioning
confidence: 99%
“…In particular, X has constant rate if r is constant on S. For general posets, the distribution of X is not uniquely determined by the UPF F (and certainly not by the rate function r). These issues and the existence of constant rate distributions are explored in [7]. A special case of a general expected value result in [7] is…”
Section: Probability Distributionsmentioning
confidence: 99%
“…These issues and the existence of constant rate distributions are explored in [7]. A special case of a general expected value result in [7] is…”
Section: Probability Distributionsmentioning
confidence: 99%