# Logistic: Create a Logistic distribution In distributions3: Probability Distributions as S3 Objects

## Description

A continuous distribution on the real line. For binary outcomes the model given by P(Y = 1 | X) = F(X β) where F is the Logistic `cdf()` is called logistic regression.

## Usage

 `1` ```Logistic(location = 0, scale = 1) ```

## Arguments

 `location` The location parameter for the distribution. For Logistic distributions, the location parameter is the mean, median and also mode. Defaults to zero. `scale` The scale parameter for the distribution. Defaults to one.

## Details

We recommend reading this documentation on https://alexpghayes.github.io/distributions3, where the math will render with additional detail and much greater clarity.

In the following, let X be a Logistic random variable with `location` = μ and `scale` = s.

Support: R, the set of all real numbers

Mean: μ

Variance: s^2 π^2 / 3

Probability density function (p.d.f):

f(x) = e^(-(t - μ) / s) / (s (1 + e^(-(t - μ) / s))^2)

Cumulative distribution function (c.d.f):

F(t) = 1 / (1 + e^(-(t - μ) / s))

Moment generating function (m.g.f):

E(e^(tX)) = = e^(μ t) β(1 - st, 1 + st)

where β(x, y) is the Beta function.

## Value

A `Logistic` object.

Other continuous distributions: `Beta`, `Cauchy`, `ChiSquare`, `Exponential`, `FisherF`, `Gamma`, `LogNormal`, `Normal`, `StudentsT`, `Tukey`, `Uniform`, `Weibull`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ```set.seed(27) X <- Logistic(2, 4) X random(X, 10) pdf(X, 2) log_pdf(X, 2) cdf(X, 4) quantile(X, 0.7) ```