On a two-parameter weighted geometric distribution: properties, computation and applications

In this article, we introduce a flexible two-parameter weighted geometric distribution characterized by its appealing properties. A key feature of this distribution is its ability to accommodate a wide range of skewness, making it particularly suitable for modeling right-skewed data. The distribution also exhibits a unimodal shape and an increasing failure rate. Several statistical measures are derived, and the distribution parameters are estimated using the method of maximum likelihood. The accuracy of these estimates is evaluated through a Monte Carlo simulation study. To demonstrate the flexibility, versatility, and practical importance of the proposed model, we analyze three real count data sets, showing its superiority over several existing models.