A ratio-type weighted geometric distribution for modelling overdispersed count data

Weighted distributions have always been a popular approach in developing flexible distributions for data modelling. In this paper, we introduce a flexible ratio-type weighted geometric distribution by adopting the geometric distribution as a basic standard distribution and opting for weights, represented as(Formula presented). The proposed distribution is overdispersed and is capable of accommodating data with small mode values such as 0, 1 and 2. The proposed distribution has the following properties – unimodal, log-concave and has increasing failure rates. The moment estimator is obtained, and the resulting estimated parameter is utilized as the initial point in finding the estimators based on the maximum likelihood technique and probability generating function. A probability comparison between the typical geometric distribution and the proposed distribution is discussed as well. A collection of insurance claim datasets is utilized for model fitting, and it was found out that generally, the proposed distribution can adequately fit the datasets as opposed to other contending distributions.