CDF for Loglogistic distribution
What is the Cumulative Distribution Function for Loglogistic distribution? I only found the Probability Density Function in the following link: https://www.mathworks.com/help/stats/loglogistic-distribution.html.
John Michell answered .
2025-11-20
cdf = e^z / (1+e^z) % the missing one pdf = (1/(sigma*x))*e^z / (1+e^z)^2 where z = (log(x)-mu)/sigma
When you make the substitution (as mentioned in wikipedia, where they use s in place of sigma)
beta = 1/sigma e^mu = alpha then e^z = (x/alpha)^beta
and for wiki,
cdf = (x/alpha)^beta) /(1+(x/alpha)^beta) pdf = (beta/alpha)*(x/alpha)^(beta-1)/(1+(x/alpha)^beta)^2