A normal scale mixture representation of the logistic distribution

In this paper it is shown that the logistic distribution can be represented as a scale mixture of the standard normal distribution where the mixing density is related to the Kolmogorov--Smirnov distribution. Two derivations of the theorem are presented that give rise to two different representations of the Kolmogorov--Smirnov distribution. The induced identity is of independent interest and is not widely published nor easily derived directly.

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Year of publication:	1991
Authors:	Stefanski, Leonard A.
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 11.1991, 1, p. 69-70
Publisher:	Elsevier
Keywords:	Kolmogorov-Smirnov distribution logistic distribution normal scale mixture

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005223504