A new probabilistic model with properties: Its implementations to the reliability and musical instruments

Probability-oriented methodologies have been firmly established and recognized as essential tools for illustrating and describing applied phenomena. Given this background, this paper delves into the development of a new probability distribution. Consequently, the main accomplishment of this paper is the development of a new probability distribution by merging the generalized Rayleigh model with a tangent-based technique. The proposed innovative model is known as the tangent generalized Rayleigh (TG-Rayleigh) distribution. The TG-Rayleigh distribution stands out for its lack of additional parameters, effectively preventing re-parameterization issues. Through mathematical derivations, certain properties and estimators for the model parameters of the TG-Rayleigh distribution are determined. The assessment of these estimators is done through a simulation study. In addition, the TG-Rayleigh distribution’s applicability and proficiency are illustrated using two specific data sets. These data sets are obtained from reliability engineering (referred to as Data 1) and music engineering (referred to as Data 2). When taking into account specific assessment criteria utilized as diagnostic tools, it becomes apparent that the TG-Rayleigh model stands out as the most effective and optimal model for analyzing Data 1 and Data 2 in comparison to other candidate probability distributions.