On the intervened generalized Poisson distribution. (English) Zbl 1093.62018
Summary: The zero-truncated Poisson distribution (ZTPD) is a model that may be appropriate when observations commence only when at least one event occurs. R. Shanmugam [Biometrics 41, 1025–1029 (1985; Zbl 0615.62020) 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. 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.
MSC:
| 62E15 | Exact distribution theory in statistics |
| 62F10 | Point estimation |
| 65C60 | Computational problems in statistics (MSC2010) |
| 62F15 | Bayesian inference |
Citations:
Zbl 0615.62020Software:
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