A new heavy-tailed distribution with identifiability and heavy-tailed properties. Empirical exploration in music engineering with a case study on piano

Abstract

The crucial role of heavy-tailed distributions in the analysis of financial and extreme value phenomena is widely acknowledged; however, there is a scarcity of probability distributions to accurately model such data. In the pursuit of analyzing financial data, researchers frequently seek out new and optimal statistical models. With a focus on this specific research domain, we present a groundbreaking model known as the new heavy-tailed exponentiated exponential distribution. The new model’s heavy-tailed behaviors are investigated through visual and mathematical methods. Estimation of the new model parameters is done through maximum likelihood estimators. Moreover, a Monte Carlo simulation study is undertaken to analyze the performance of estimators. In our study, we examine two specific data sets pertaining to the price quotations of Yamaha pianos in the United States to present the new distribution. The first set of data focuses on the prices of Yamaha upright pianos, while the second set highlights the prices of Yamaha Clavinova digital pianos. By conducting four evaluation tests, we evaluate the fitting performance of the NHTE-exponential distribution against the rival distributions.

Keywords

• Exponential distribution
• Heavy-tailed distributions
• Identifiability
• Music engineering
• Piano
• Price quotations