1Alhaji Modu Isa, 2Mustapha Mohammed Karagama and 3Alhaji Ismaila Sulaiman
Department of Mathematics and Computer Science, Borno State University, Maiduguri, Nigeria
Department of Mathematics, University of Maiduguri, Borno State, Nigeria
Department of Mathematics, Nasarawa State University, Keffi, Nigeria
*Corresponding author’s Email: alhajimoduisa@bosu.edu.ng, doi.org/10.55639/607.222120
ABSTRACT
Probability distributions are fundamental tools in statistical modeling and data analysis, providing a mathematical framework to describe the behavior of random variables. However, a significant challenge lies in identifying and utilizing a distribution that accurately captures the complexities of diverse real-world data. Many existing distributions may offer robust solutions for specific types of data but fail to generalize across various datasets with different characteristics, such as varying degrees of skewness, kurtosis, and tail behavior. This study was motivated by the attractiveness and flexibility of the Cosine-G family of distributions and the established utility of the Inverse Exponential distribution in various real-life datasets. The research introduces a compound distribution by combining the Cosine-G family of distribution and the Inverse Exponential distribution, resulting in the creation of the Cosine Inverse Exponential distribution. The study explores numerous properties of the newly proposed model, including moments, hazard functions, survival functions, reverse hazard function, cumulative hazard function, and quantile function. The parameters of the model were estimated using the method of maximum likelihood estimate. Exploratory data analysis was conducted on the dataset to examine its characteristics. These datasets exhibited varying degrees of kurtosis and skewness. The proposed model was applied to these datasets and compared with existing distributions. The results demonstrate that the proposed model outperforms its competitors, highlighting its superior flexibility.
Keywords:
Cosine-G,
Inverse-Exponential
distribution,
Reliability Analysis,
Maximum-Likelihood
Estimate,