A new Marshall-Olkin generalized-k family of distributions with applications

Abstract In this article, we describe a new Marshall-Olkin family of distributions based on the Marshall-Olkin family of distributions by employing a different generator. We have derived several statistical properties of the new Marshall-Olkin family, including survival function, hazard rate function, quantile function, moments, and linear representation. We have taken the Weibull distribution as a baseline distribution and found that the new Marshall-Olkin Weibull distribution exhibits a variety of shapes for its hazard rates and densities. We have tested the performance of various estimation methods for the new Marshall-Olkin family of distributions, including eight different estimation methods. Additionally, we conducted extensive simulations to assess the robustness of the estimation methods across various scenarios and determine which methods are most effective for varying sample sizes. To further validate the new Marshall-Olkin Weibull distribution, we have used two different data sets to compare the fitted new Marshall-Olkin Weibull distribution with the well-known comparative models. By testing the performance of different estimation methods and using multiple data sets, we can demonstrate the versatility and usefulness of the new Marshall-Olkin family of distributions for modeling a wide range of phenomena.