Abstract
The zero-truncated Poisson distribution (ZTPD) is a model that may be appropriate when observations commence only when at least one event occurs. Shanmugam (1985) introduced the intervened Poisson distribution (IPD) as a replacement for the ZTPD in situations when some intervention process may alter the mean of the rare event generating process under observation. Both of these zero-truncated distributions are underdispersed. In this paper, we discuss an intervened generalized Poisson distribution (IGPD) that extends the IPD, and that may be either underdispersed or overdispersed. Two numerical illustrations are included, one of which features a Bayesian analysis.
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