distributional (version 0.5.0)

dist_logistic: The Logistic distribution

Description

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

Usage

dist_logistic(location, scale)

Arguments

location, scale

location and scale parameters.

Details

We recommend reading this documentation on https://pkg.mitchelloharawild.com/distributional/, where the math will render nicely.

In the following, let $X$ be a Logistic random variable with location = $\mu$ and scale = $s$.

Support: $R$, the set of all real numbers

Mean: $\mu$

Variance: $s^2{\pi }^2/3$

Probability density function (p.d.f):

$$f(x)=\frac{e^{-(\frac{x-\mu }{s})}}{s[1+\exp (-(\frac{x-\mu }{s})){]}^2}$$

Cumulative distribution function (c.d.f):

$$F(t)=\frac{1}{1+e^{-(\frac{t-\mu }{s})}}$$

Moment generating function (m.g.f):

$$E(e^{tX})=e^{\mu t}\beta (1-st,1+st)$$

where $\beta (x,y)$ is the Beta function.

See Also

stats::Logistic

Examples

dist <- dist_logistic(location = c(5,9,9,6,2), scale = c(2,3,4,2,1))

dist
mean(dist)
variance(dist)
skewness(dist)
kurtosis(dist)

generate(dist, 10)

density(dist, 2)
density(dist, 2, log = TRUE)

cdf(dist, 4)

quantile(dist, 0.7)