New discrete trigonometric distributions: estimation with application to count data

In this research, we contribute to the development of original discrete distributions for count data analysis. We elaborate four new and different discrete trigonometric distributions with two parameters based on a discretization of the so-called sin-Weibull, cos-Weibull, tan-Weibull, and type II tan-Weibull distributions. We investigate the advantages of the proposed distributions and their trigonometric nature for capturing count data. In particular, some fundamental distributional properties of the discrete sin-Weibull distribution are derived. Subsequently, we turn it into a statistical model. Parameter estimation by the maximum likelihood and proportion of zeros and ones methods are then discussed. A simulation study is carried out to evaluate some frequentist properties of the developed methodology. As the study focuses mainly on the practical aspect, the applicability of the proposed models is evaluated using real-count datasets from various fields.