CDF for Loglogistic distribution

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