A new probabilistic model with reliability properties and empirical analysis in musical education: A case study centered on piano

This study mainly aims to enhance the current knowledge base of distribution theory by revealing a new probability distribution known as the cosine-weighted generalized inverse Weibull (CWGI-Weibull) distribution. Thus, this effort seeks to improve data modeling methodologies and tactics, ultimately bolstering decision-making abilities in practical research. The development of the CWGI-Weibull distribution results from using the generalized inverse Weibull distribution with an existing cosine-based distributional method. Along with showcasing certain distributional functions and visual illustrations, different mathematical properties are derived for the CWGI-Weibull distribution. Moreover, the method for parameter estimation and the related simulation study of the CWGI-Weibull distribution are included as well. The findings from the simulation study indicate that the estimators for the CWGI-Weibull distribution are both efficient and consistent, getting closer to the actual values as the sample size increases. Finally, a practical application of the CWGI-Weibull distribution is analyzed to demonstrate its advantages over several modifications of the Rayleigh distribution. To achieve this, we focus on a case study from music education concerning the price quotes of pianos. Through quantitative assessment tests, we discover that the CWGI-Weibull distribution outperforms the competing distributions and proves to be the most efficient for analyzing piano price quotes.