On Intervened Stuttering Poisson Distribution and Its Applications
Intervened Poisson distribution (IPD) has been found suitable for dealing with intervention problems in medical situations where positive Poisson distribution fails. Kumar and Shibu (2011a) introduced a modified version of IPD, namely, MIPD, to deal situations of two interventions. Through this article we propose an extended form of this modified version, namely, the intervened stuttering Poisson distribution (ISPD), appropriate for situations of more than two interventions. An important characteristic of ISPD over IPD and MIPD is that it is both underdispersed and overdispersed for particular values of its parameters and hence more suitable for practical situations. Here, we study some important properties of ISPD and discuss the estimation of its parameters by method of factorial moments and maximum likelihood. Some real-life data sets are given to illustrate that ISPD gives the best fit compared to the existing models.
KeywordsFactorial moments Maximum likelihood estimation Positive Poisson distribution Probability generating function stuttering Poisson distribution
AMS (2000) subject classificationPrimary 60E05 60E10
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