An Inquiry into the Nature of Frequency Distributions Representative of Multiple Happenings with Particular Reference to the Occurrence of Multiple Attacks of Disease or of Repeated Accidents

Greenwood, M.; Yule, George

doi:10.2307/2341080

Cited by 751 publications

(296 citation statements)

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“…Other assumptions are possible, but do not reduce to closed form, and thus require more complicated estimation procedures (see Schoenberg, 1985). Greenwood and Yule (1920) first derived the new distribution, called the negative binomial, by adding this additional first principle (hi following a gamma distribution) to the initial four with the following procedure. First, derive the joint distribution ifi) of Yi and Xi (both now random variables) using the basic rule for conditional probability…”

Section: Modeling Event Counts With Overdispersionmentioning

confidence: 99%

Variance Specification in Event Count Models: From Restrictive Assumptions to a Generalized Estimator

King¹

1989

American Journal of Political Science

253

145

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This paper discusses the problem of variance specification in models for event count data. Event counts are dependent variables that can take on only nonnegative integer values, such as the number of wars or coups d'etat in a year. I discuss several generalizations of the Poisson regression model, presented in King (1988), to allow for substantively interesting stochastic processes that do not fit into the Poisson framework. Individual models that cope with, and help analyze, heterogeneity, contagion. and negative contagion are each shown to lead to specific statistical models for event count data. In addition. I derive a new generalized event count (GEC) model that enables researchers to extract significant amounts of new information from existing data by estimating features of these unobserved substantive processes. Applications of this model to congressional challenges of presidential vetoes and superpower conflict demonstrate the dramatic advantages of this approach.

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Section: Modeling Event Counts With Overdispersionmentioning

confidence: 99%

Variance Specification in Event Count Models: From Restrictive Assumptions to a Generalized Estimator

King¹

1989

American Journal of Political Science

253

145

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“…Heterogeneity in connection with Poisson processes was in fact studied as early as 1920 by Greenwood and Yule [27], who used a compound Poisson distribution. Later, Maguire, Pearson and Wynn [50], studying occurrences of industrial accidents, showed how Laplace transforms enter general expressions for resulting distributions of intervals and counts.…”

Section: Unobserved Heterogeneity In Repairable Systemsmentioning

confidence: 99%

Statistical Modeling and Analysis of Repairable Systems

Lindqvist

1999

Statistical and Probabilistic Models in Reliability

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Abstract. We review basic modeling approaches for failure and maintenance data from repairable systems. In particular we consider imperfect repair models, defined in terms of virtual age processes, and the trend-renewal process which extends the nonhomogeneous Poisson process and the renewal process. In the case where several systems of the same kind are observed, we show how observed covariates and unobserved heterogeneity can be included in the models. We also consider various approaches to trend testing. Modern reliability data bases usually contain information on the type of failure, the type of maintenance and so forth in addition to the failure times themselves. Basing our work on recent literature we present a framework where the observed events are modeled as marked point processes, with marks labeling the types of events. Throughout the paper the emphasis is more on modeling than on statistical inference.

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“…It is well known that the parameter in a Poisson distribution is considered to be a gamma variate in the famous article by Greenwood and Yule (1920). Skellam (1948) derived a probability distribution from the binomial distribution by regarding the probability of success as a beta variable between sets of trials.…”

Section: Introductionmentioning

confidence: 99%