CDF for Loglogistic distribution

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Zhengpu Chen
Zhengpu Chen 2018-11-8
编辑： David Goodmanson 2018-11-9
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.
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Walter Roberson
Walter Roberson 2018-11-8
https://en.m.wikipedia.org/wiki/Log-logistic_distribution
Zhengpu Chen
Zhengpu Chen 2018-11-8
编辑：Walter Roberson 2018-11-8
Thank you for the reply. The expression of the function in Wiki and the one in Matlab documentation https://www.mathworks.com/help/stats/loglogistic-distribution.html seem to be not the same. I don't know if they are equivalent.

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David Goodmanson
David Goodmanson 2018-11-9
编辑：David Goodmanson 2018-11-9
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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