The zero-distorted Topp-Leone geometric distribution: some properties and its applications with biological data

Abstract

In this paper, the zero-distorted Topp-Leone geometric distribution is introduced. It belongs to the k-distorted generalized discrete family of distributions. This family is useful to fit both zero-inflated and zero-deflated data. We also derive the first four moments and index of dispersion for the zero-distorted Topp-Leone geometric distribution. For parameter estimation, the most well-known method called the maximum likelihood estimation is utilized. In application study, we apply the proposed model to fit with three biological datasets. Furthermore, the fitted results of zero-distorted Topp-Leone geometric distribution are compared with the Topp-Leone geometric, the zero-distorted generalized geometric and the negative binomial distributions. In conclusion, the Anderson-Darling test statistic for discrete distributions shows that the zero-distorted Topp-Leone geometric distribution is the most appropriate model for these datasets.