A New Alpha Power Cosine-Weibull Model with Applications to Hydrological and Engineering Data

Abstract

Modifying the existing probability models in the literature and introducing new extensions of the existing probability models is a prominent and interesting research topic. However, in the most recent era, the extensions of the probability models via trigonometry methods have received great attention. This paper also offers a novel trigonometric version of the Weibull model called a new alpha power cosine-Weibull (for short, “NACos-Weibull”) distribution. The NACos-Weibull distribution is introduced by incorporating the cosine function. Certain distributional properties of the NACos-Weibull model are derived. The estimators of the NACos-Weibull model are derived by implementing the maximum likelihood approach. Three simulation studies are provided for different values of the parameters of the NACos-Weibull distribution. Finally, to demonstrate the effectiveness of the NACos-Weibull model, three applications from the hydrological and engineering sectors are considered.

Keywords

• Weibull model
• trigonometric function
• distributional properties
• simulation study
• flood peaks data
• failure times data