Marshall-Olkin Cosine Topp-Leone Family of Distributions with Application to Real-life Datasets

Abstract The Marshall-Olkin (MO) family of distributions is a flexible framework that is adept at modeling complex dependence structures and tail behaviors in a variety of real-life datasets. This paper introduces a new member of the MO family called the Marshall-Olkin Cosine Topp-Leone G family. We derive several mathematical properties of this family, including the moment, moment generating function, Renyi's entropy, and the distribution of order statistics. We also provide some special cases of this class. To estimate the model parameters, we use the method of maximum likelihood. We explore the performance of this method through simulation studies, which show that biases and root-mean-square errors decrease as the sample size increases. To demonstrate the usefulness of our model, we apply it to two real-world datasets. Our findings show that, in comparison with existing distributions, our model provides the best fit for these data.