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Logistic Distribution

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Calculate the probability density function, lower cumulative probability, and upper cumulative probability of the logistic distribution.
Percentile x
Location parameter a
Scale parameter b
b＞0
\(\normalsize Logistic\ distribution\\ (1)\ probability\ density\\ \hspace{30px}f(x,a,b)={\large\frac{1}{b}\frac{e^{-\frac{\small{x}-a}{b}}}{(1+e^{-\frac{\small{x}-a}{b}})^2}}\\ (2)\ lower\ cumulative\ distribution\\ \hspace{30px}P(x,a,b)={\large\int_{\small-\infty}^{\small x}}f(t,a,b)dt\\ (3)\ upper\ cumulative\ distribution\\ \hspace{30px}Q(x,a,b)={\large\int_{\small x}^{\small\infty}}f(t,a,b)dt\\\)

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