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A normal scale mixture representation of the logistic distribution

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  • Stefanski, Leonard A.

Abstract

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.

Suggested Citation

  • Stefanski, Leonard A., 1991. "A normal scale mixture representation of the logistic distribution," Statistics & Probability Letters, Elsevier, vol. 11(1), pages 69-70, January.
    • Handle: RePEc:eee:stapro:v:11:y:1991:i:1:p:69-70
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    Cited by:

    1. Peter Carr & Lorenzo Torricelli, 2021. "Additive logistic processes in option pricing," Finance and Stochastics, Springer, vol. 25(4), pages 689-724, October.
    2. S. Rao Jammalamadaka & Tomasz J. Kozubowski, 2017. "A General Approach for Obtaining Wrapped Circular Distributions via Mixtures," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 79(1), pages 133-157, February.
    3. Rubio, Francisco Javier & Liseo, Brunero, 2014. "On the independence Jeffreys prior for skew-symmetric models," Statistics & Probability Letters, Elsevier, vol. 85(C), pages 91-97.

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