The Tail Characteristics of Several Asymmetric Distributions and Their Applications in the Field of Financial Data Modelling and Machine Learning

Abstract

Asymmetric distributions play a pivotal role in various fields, including finance, machine learning, and artificial intelligence. In finance, asymmetric distributions, characterized by negative skewness, peakedness, heavy tails, and asymmetric fluctuations, provide a more accurate representation of financial data. These distributions are particularly useful in capturing the complex behavior of assets and risk management. In the field of machine learning, data disturbance, noise, outliers and other disturbances will have a negative impact on the performance and reliability of the model, asymmetric distributions offer a valuable tool for describing the tail behavior of noise and interference. This is crucial in designing more robust machine learning models that can handle outliers and noise effectively. Additionally, when dealing with unbalanced data classification, asymmetric distributions can be leveraged by adjusting the decision threshold of classifiers or employing specialized loss functions. In this paper, the asymptotic tail ratio behavior of probability density function(pdf) and cumulative distribution function (cdf) of three asymmetric distributions (asymmetric Laplace, generalized Logistic and asymmetric normal distribution) and Student-t distribution were considered respectively under some regular conditions. The detailed characteristics of these asymmetric tails will have a profound impact on the fields of financial data analysis, artificial intelligence, and unbalanced classification.