A new probabilistic model with properties and Monte Carlo simulation: Its explorations in dance education and music engineering

Abstract

In the examination of real-life situations, the application of probability distributions is often crucial for statistical analysis of the real-life scenarios. Many models based on probability have been utilized in disciplines such as music education, music engineering, and other music-related areas. Hence, acknowledging the significance of probability-based approaches, this article introduces an innovative probability model known as a new generalized Rayleigh distribution. The suggested model is established on merging the generalized Rayleigh distribution with a prominent weighted probabilistic method. The mathematical properties, specifically the quartile-based features of the novel generalized Rayleigh distribution, are investigated. Moreover, we outline the derivation of the point estimators for the unknown parameters of the new model. A thorough simulation study is also conducted to examine the performances of these point estimators. Within the music industry, specifically in music education and music engineering, we examine the practical implications of the new generalized Rayleigh distribution. We observe that it offers a superior fit when contrasted with other distributions. Our findings demonstrate that the new distribution is a inclusion to the group of probability distributions that can be applied in music engineering and other closely connected engineering fields for the statistical analysis of real-life events.