Intensive natural distribution as Bernoulli success ratio extension to continuous: enhanced Gaussian, continuous Poisson, and phenomena explanation

TL;DR

This paper introduces the intensive natural distribution, a new statistical model based on Bernoulli success ratios, extending to continuous variables like Gaussian and Poisson, with applications in explaining phenomena and fitting empirical data.

Contribution

The paper presents a novel distribution that unifies and extends existing models, providing a theoretical foundation and demonstrating its effectiveness with real-world data.

Findings

Successfully explained the Horwitz curve.

Effectively fitted histograms and probability charts from diverse data.

Maintained robustness across various measurement types.

Abstract

A new distribution named intensive natural distribution is introduced with the intent of consolidating statistics and empirical data. Based on the probability derived from the Bernoulli distribution, this method extended also Poisson distribution to continuous, preserving its skewness. Using this model, the Horwitz curve has been explained. The theoretical derivation of our method, which applies to every kind of measurements collected through sampling, is here supported by a mathematical demonstration and illustrated with several applications to real data collected from chemical and geotechnical fields. We compared the proposed intensive natural distribution to other widely used frequency functions to test the robustness of the proposed method in fitting the histograms and the probability charts obtained from various intensive variables.