One and two side generalisations of the log-Normal distribution by means of a new product definition

TL;DR

This paper introduces a generalized log-Normal distribution based on a q-product modification of the Kaypten process, which adjusts tail behavior and is applicable to biological and financial data.

Contribution

It presents a new generalized distribution inspired by q-product modifications, including statistical features, random number generators, and real-world applications.

Findings

Distribution adjusts tail behavior based on q parameter

Provides statistical tools and quantile tables for the new distribution

Demonstrates applicability to biological and financial data

Abstract

In this manuscript we introduce a generalisation of the log-Normal distribution that is inspired by a modification of the Kaypten multiplicative process using the $q$-product of Borges [Physica A \textbf{340}, 95 (2004)]. Depending on the value of q the distribution increases the tail for small (when $q<1$) or large (when $q>1$) values of the variable upon analysis. The usual log-Normal distribution is retrieved when $q=1$. The main statistical features of this distribution are presented as well as a related random number generators and tables of quantiles of the Kolmogorov-Smirnov. Lastly, we illustrate the application of this distribution studying the adjustment of a set of variables of biological and financial origin.