MATLAB: CDF for Loglogistic distribution

cdfloglogistic 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.

Best Answer

Hello ZC,
They are equivalent. In Matlab
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
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