论文信息 - A normal scale mixture representation of the logistic distribution

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.

Leonard A. Stefanski

[1] W. Feller. On the Kolmogorov–Smirnov Limit Theorems for Empirical Distributions , 1948 .

[2] N. Smirnov. Table for Estimating the Goodness of Fit of Empirical Distributions , 1948 .

[3] Raymond J. Carroll,et al. On errors-in-variables for binary regression models , 1984 .