The Two-Piece Normal, Binormal, or Double Gaussian Distribution: Its Origin and Rediscoveries

TL;DR

This paper explores the historical development and rediscoveries of the two-piece normal distribution, clarifying its origins and addressing misconceptions about its originality.

Contribution

It provides a detailed historical analysis of the two-piece normal distribution and corrects misconceptions regarding its attribution.

Findings

Clarifies the origin of the two-piece normal distribution in Fechner's work

Highlights the misattribution by Pearson and Sheynin

Documents the rediscoveries and generalisations of the distribution

Abstract

This paper traces the history of the two-piece normal distribution from its origin in the posthumous Kollektivmasslehre (1897) of Gustav Theodor Fechner to its rediscoveries and generalisations. The denial of Fechner's originality by Karl Pearson, reiterated a century later by Oscar Sheynin, is shown to be without foundation.