Abstract. The objective of this paper is to provide an alternative distribution for modeling overdispersed count data. We propose a negative binomial-Crack (NB-CR) distribution which is obtained by mixing the NB distribution with a CR distribution. This new formulation distribution contains as special cases three parameter distribution, namely, negative binomial-inverse Gaussian (NB-IG), negative binomial-Birnbaum-Saunders (NB-BS) and negative binomial-length biased inverse Gaussian (NB-LBIG). In addition, we present some properties of the new distribution such as the factorial moments, the first four moments, variance, skewness and kurtosis. Parameters estimation are also implemented using maximum likelihood method and the application of NB-CR distribution is carried out on a sample of count data. The results show that the NB-CR provides a better fit compared to the Poisson and the NB distribution.

Received: December 23, 2012

AMS Subject Classification: 60E05

Key Words and Phrases: mixed negative binomial distribution, negative binomial-crack distribution, count data, overdispersion

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