The enhanced fitting ability of a new tangent-apt probabilistic model: Its implementations to the music engineering and reliability phenomena

Abstract

It is an established and already accomplished fact that probability-based methodologies (or probability/statistical distributions) play the roles of imperative tools in illustrating and describing applied phenomena. Paying attention to these previous facts, this paper considers the evolution of a new probability distribution. Thus, the main achievement of this paper leads to a new probability distribution as a result of combining the exponentiated exponential model with a tangent-based stratagem. The new model is called the tangent exponentiated exponential (TEE) distribution. For the TEE distribution, certain distributional properties and estimators of the model parameters are derived mathematically. The appraisal of the estimators of the TEE distribution is accomplished through a simulation study. Moreover, the applicability and virtuoso of the TEE distribution are exemplified via two data sets, which are taken from the music engineering (named Data 1) and reliability sector (named Data 2). By considering the p-value and three other important statistical tests/methods as diagnostic tools, we find that the TEE distribution is the most useful and optimal model for Data 1 and Data 2 compared to certain candidate probability distributions.

Keywords

• Exponentiated exponential distribution
• Tangent-based tactics
• Monte Carlo simulation
• Music engineering
• Reliability
• Statistical analysis