dist_logistic
The Logistic distribution
Description
![[Stable]](../help/figures/lifecycle-stable.svg)
Usage
dist_logistic(location, scale)
Arguments
location |
location and scale parameters. |
scale |
location and scale parameters. |
Details
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.
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 = 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.
See Also
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)