A New Class of Skewed Bimodal Distributions

TL;DR

This paper introduces a novel method for creating skewed bimodal distributions by transforming symmetric unimodal densities without relying on the cumulative distribution function, and then distorting their unimodality.

Contribution

It presents a new skewing mechanism that alters the scale on each side of the mode, enabling the generation of skewed bimodal distributions without traditional CDF-based methods.

Findings

New class of skewed bimodal distributions proposed

Method avoids reliance on cumulative distribution functions

Potential applications in modeling asymmetric data

Abstract

In this paper, we propose to obtain the skewed version of a unimodal symmetric density using a skewing mechanism that is not based on a cumulative distribution function. Then we disturb the unimodality of the resulting skewed density. In order to introduce skewness we use the general method which transforms any continuous unimodal and symmetric distribution into a skewed one by changing the scale at each side of the mode.