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

 Logistic R Documentation

## Create a Logistic distribution

### 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

```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()`, `Erlang()`, `Exponential()`, `FisherF()`, `Frechet()`, `GEV()`, `GP()`, `Gamma()`, `Gumbel()`, `LogNormal()`, `Normal()`, `RevWeibull()`, `StudentsT()`, `Tukey()`, `Uniform()`, `Weibull()`

### Examples

```
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)
```

distributions3 documentation built on Sept. 7, 2022, 5:07 p.m.