A new discrete distribution with actuarial applications

A new discrete distribution depending on two parameters, α < 1 , α ≠ 0 and 0 < θ < 1 , is introduced in this paper. The new distribution is unimodal with a zero vertex and overdispersion (mean larger than the variance) and underdispersion (mean lower than the variance) are encountered depending on the values of its parameters. Besides, an equation for the probability density function of the compound version, when the claim severities are discrete is derived. The particular case obtained when α tends to zero is reduced to the geometric distribution. Thus, the geometric distribution can be considered as a limiting case of the new distribution. After reviewing some of its properties, we investigated the problem of parameter estimation. Expected frequencies were calculated for numerous examples, including short and long tailed count data, providing a very satisfactory fit.