Analysis of Cauchy Distribution and Its Applications

Cauchy distribution is a continuous probability distribution with heavy tails and undefined mean and variance. Following the proposal that intends to research properties, applications, and consequences in physics, finance, and signal processing will be dedicated to the Cauchy distribution. Five numerical examples are provided showing various properties of the Cauchy distribution. The first example will be devoted to a problem of generating random variables, Cauchy-distributed; subsequent examples consider some applications: modeling resonance phenomena, analysis of stock prices, and noise simulation in signal processing. We illustrate some peculiar properties of the Cauchy distribution by simulations and statistical analysis: stability under convolution and a heavy tail. We hope that by the end of this work, the understanding of the Cauchy distribution would be taken a notch higher, where its importance in real-life situations with outliers or extreme values cannot be overemphasized. We shall present our results, assisted by visualization such as histograms and Q-Q plots, which will showcase the nature of this distribution. In simple words, this proposal would delve deep to undertake a look at what is called the Cauchy distribution, showing its relevance and applicability in statistical modeling and analysis.