The Beta Transmuted Mukherjee-Islam Distribution:Estimation and Applications

Abstract

This research proposes a novel five-parameter statistical distribution called the Beta Transmuted Mukherjee-Islam (BTM-I) distribution. This distribution has been developed to enhance the capability and flexibility of statistical modeling for various data characteristics. It integrates the Beta technique and the quadratic rank transmutation map method with the Mukherjee-Islam distribution. The proposed distribution encompasses several competing models as special cases and is characterized by five parameters, making it more flexible in representing diverse data types.

The study derives the mathematical properties of the new distribution, including moments, moment generating function, mean deviation, order statistics, and reliability analysis. The estimation of the parameters is performed using the Maximum Likelihood method (MLE). The accuracy of these estimators is evaluated through an extensive simulation study of key performance metrics like Bias, Standard Error (SE), and Mean Squared Error (MSE). Crucial measures for assessing confidence intervals, such as Coverage Probability (CP) and Coverage Length (CL), were also utilized. The results demonstrated that the maximum likelihood estimators were consistent and the obtained CP and CL values were satisfactory, confirming the reliability and effectiveness of the estimations.

The study also includes a practical application to three real-world datasets to illustrate the significance, efficiency, and utility of the proposed distribution. The performance of the BTM-I distribution was compared to that of several competing statistical models. The results conclusively showed that the BTM-I distribution possesses superior flexibility that enables it to effectively model various types of data and outperform the competing models. These findings confirm that the BTM-I distribution is a robust and effective tool and represents a valuable addition for statisticians and researchers across multiple fields.