Heterogeneous Weibull count distribution

Abstract

In this paper, we present a generalized model for count data based upon an assumed Weibull interarrival times. Weibull interarrival times could handle overdispersed data with shape parameter 0 < c < 1, and underdispersed data with c > 1, and is reduced as exponential when c = 1. Weibull count model will be obtained by Taylor expansion and convolution method. By mixing, we obtain heterogeneous Weibull count model. Finally, we fit this model and several other models to non-equidispersed data and show that this model fit the data better than Poisson.