Logistic distribution

Logistic distribution
Probability density function
Standard logistic PDF
Cumulative distribution function
Standard logistic CDF
Parameters location (real)
scale (real)
Support
PDF
CDF
Quantile
Mean
Median
Mode
Variance
Skewness
Excess kurtosis
Entropy
MGF
for
and is the Beta function
CF
Expected shortfall
where is the binary entropy function[1]

In probability theory and statistics, the logistic distribution is a continuous probability distribution. Its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks. It resembles the normal distribution in shape but has heavier tails (higher kurtosis). The logistic distribution is a special case of the Tukey lambda distribution.

  1. ^ Norton, Matthew; Khokhlov, Valentyn; Uryasev, Stan (2019). "Calculating CVaR and bPOE for common probability distributions with application to portfolio optimization and density estimation" (PDF). Annals of Operations Research. 299 (1–2). Springer: 1281–1315. doi:10.1007/s10479-019-03373-1. Archived from the original (PDF) on Mar 1, 2023. Retrieved 2023-02-27.