The polar-generalized normal distribution

TL;DR

This paper introduces the polar-generalized normal distribution, an extension of the normal distribution that captures bimodality and asymmetry, with explicit formulas and Bayesian estimation methods demonstrated on real and simulated data.

Contribution

It presents a novel distribution extending the normal distribution to model bimodal and asymmetric data, with explicit formulas and Bayesian estimation techniques.

Findings

Successfully models asymmetric bimodal data

Provides explicit formulas for distribution functions and moments

Demonstrates effectiveness on real and simulated datasets

Abstract

This paper introduces an extension to the normal distribution through the polar method to capture bimodality and asymmetry, which are often observed characteristics of empirical data. The later two features are entirely controlled by a separate scalar parameter. Explicit expressions for the cumulative distribution function, the density function and the moments were derived. The stochastic representation of the distribution facilitates implementing Bayesian estimation via the Markov chain Monte Carlo methods. Some real-life data as well as simulated data are analyzed to illustrate the flexibility of the distribution for modeling asymmetric bimodality.