A new probabilistic approach with properties and statistical evaluation using the teacher’s rating and reliability data

Abstract

When analyzing real-life contexts, the application of probability distributions is frequently essential for effective statistical analysis. Many probability models have been adopted in practical disciplines, notably in the educational sector and reliability engineering. As a result, recognizing the significance of probability-centric strategies in the statistical assessment of real-life events, this article puts forth a new probability model termed the modified exponentiated Weibull (ME-Weibull) distribution. The study explores the mathematical properties, especially the quartile-oriented features of the ME-Weibull distribution. In addition, we provide a comprehensive derivation of the point estimators for the unknown parameters of the ME-Weibull distribution. In the fields of education and reliability engineering, we delve into the analysis of three practical data sets to illustrate the significant implications of the ME-Weibull distribution. The first data set outlines the performance ratings attributed to the teacher, while the other two data sets focus on the failure times associated with electronic components. To provide a comprehensive understanding of the ME-Weibull distribution’s effectiveness, we conduct a thorough comparison with other adversarial distributions commonly used in applied fields. Analysis of the p-value along with three other statistical tests reveals that the ME-Weibull distribution provides the most accurate representation of the data examined.

Keywords

• Exponentiated Weibull distribution
• Mathematical properties
• Estimation
• Performance rating
• Reliability engineering
• Statistical modeling