An alternative statistical model for modeling the bimodal asymmetric data with properties, copulas, assessment and applications

This study derives and investigates an extension of the Chen distribution that extends it in a new and flexible way. The well-known Chen distribution, which is renowned for its high level of adaptability and a wide variety of potential applications, was utilized as the foundation for creating the new model. The newly derived hazard rate can be defined as "monotonically increasing", "bathtub", "upside-down", "upsidedown-constant-increasing", "J hazard rate", or "bathtub". Other possible descriptions include "monotonically decreasing", "bathtub", "upside-down", "upside down-constant-increasing", and "upside down". Other terms that could describe it are "monotonically decreasing"and "bathtub". It is possible to determine the pertinent statistical features, such as the mean of the remaining life, the mean of the past lifespan, raw and central moments, conditional moments, and the mean. Some examples of the bivariate extensions that we developed are presented. Finally, we studied and analyzed two data sets to demonstrate the new model's relevance, flexibility, and applicability.