On the discrete Sin-Lindley distribution and its applications

Abstract This article introduces new one-parameter discrete trigonometric distributions for analyzing count data. In particular, it focuses on a simple, one-parameter discrete trigonometric version of the Lindley distribution, known as the discrete Sin-Lindley distribution. The key mathematical properties are derived, including the probability mass function, cumulative distribution function, quantile function, probability generating function, moments, skewness, kurtosis, and order statistics. The maximum likelihood approach is then employed to estimate the unique parameter. Simulation studies demonstrate the effectiveness of the new model across varying sample sizes. The applicability and robustness of the model are demonstrated by analyzing five real-world datasets and by comparing it with Lindley-related distributions and discrete trigonometric distributions, highlighting its potential in statistical analysis.