On some aspects of intervened generalized Hermite distribution

Summary The intervened Poisson distribution (IPD) of Shanmugam (Biometrics 41:1025–1029, <CitationRef CitationID="CR19">1985</CitationRef>) has been found suitable for some rare event situations where some intervention arises. The main drawback of IPD is that it is under-dispersed and appropriate for single intervention situation. Through this paper, we introduce a general class of distributions, which includes IPD as its special case, suitable for situations of under-dispersed, over-dispersed and multiple intervention cases. Several properties of this new class of intervened distribution are investigated and illustrated its usefulness with the help of real life data sets. Copyright Sapienza Università di Roma 2013