# Logistic distribution Probabilities

Calculator of Logistic distribution : probabilities, density function (PDF) and cumulative density function (CDF).

## Logistic Distribution formulas

X : a random variable following a logistic distribution

`mu` : location parameter

s : scale parameter (s > 0)

### Probability Density Function (PDF)

`f(x) = (e^(-(x-mu))/s)/(s*(1+e^(-(x-mu))/s)^2)`

### Cumulative distribution function (CDF)

`F(x) = \int_-oo^x f(t)\ dt`

`F(x) = 1/(1+e^(-(x-mu))/s)`

### Probabilities

Probability that X is greater than a :

`P(X > a) = 1 - F(a) = 1/(1+e^(a-mu)/s)`

Probability that X is less than b :

`P(X < b) = F(b) = 1/(1+e^(mu-b)/s)`

Probability that X lies between a and b :

`P(a < X < b) = F(b) - F(a)`

## See also

Inverse Logistic distribution

Logistic distribution Chart

Statistics Calculators