A novel probability model: Mathematical properties and assessment in music therapy and reliability

The critical significance of probability distributions in the analysis of real-world phenomena is broadly recognized; however, there is a lack of probability distributions capable of effectively modeling practical data sets. In the quest to analyze real data, researchers often strive to discover new and more effective statistical models. Consequently, numerous probability-based methodologies are created and applied. A majority of these methodologies rely on the introduction of new parameters, which can occasionally result in re-parameterizations. Focusing on this particular research domain, we unveil a new statistical methodology intended to enhance the distributional flexibility of probability distributions. This methodology, which incorporates arcsine and sine functions, is known as the arcsine-sine-G (ASS-G) method. Informed by the ASS-G method, a new variant of the exponentiated exponential distribution has been established, called the arcsine-sine-exponentiated exponential (ASSE-exponential) distribution. Estimators associated with the ASSE-exponential distribution have been successfully obtained. Their performance is scrutinized through a simulation study. In addition, properties concerning quartiles and identifiability are derived. Ultimately, the relevance of the ASSE-exponential distribution is established by examining two data sets sourced from music therapy and reliability engineering. Based on certain evaluation tests, we show the fitting performance of the ASSE-exponential distribution against the rival models.