Abstract

This study presents the cosine Gompertz (COG) distribution, which is developed by integrating the cosine generator with the traditional Gompertz distribution. The research explores various statistical characteristics of the COG distribution, and the model parameters are estimated using the maximum likelihood estimation method. It is shown that the hazard rate function of the COG distribution increases monotonically. The probability density function (PDF) of the COG distribution exhibits a range of shapes, including increasing-decreasing, approximately symmetric, and right-skewed patterns. Monte Carlo simulations demonstrate that the estimators for the COG model are consistent, as evidenced by the observed reduction in absolute bias and root mean square error with increasing sample sizes, indicating improved accuracy of the estimators as the number of observations grows. The COG distribution is tested on two real-life datasets and compared with other existing lifetime distributions. The findings suggest that the COG distribution offers a superior fit to both datasets compared to the alternative distributions.

Key words: Cosine G, Gompertz Distribution, Quantile Function, Moment, Maximum Likelihood Estimation