dist_logistic {distributional}R Documentation

The Logistic distribution

Description

[Stable]

A continuous distribution on the real line. For binary outcomes the model given by P(Y=1X)=F(Xβ)P(Y = 1 | X) = F(X \beta) where FF 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 XX be a Logistic random variable with location = μ\mu and scale = ss.

Support: RR, the set of all real numbers

Mean: μ\mu

Variance: s2π2/3s^2 \pi^2 / 3

Probability density function (p.d.f):

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

Cumulative distribution function (c.d.f):

F(t)=11+e(tμs) F(t) = \frac{1}{1 + e^{-(\frac{t - \mu}{s})}}

Moment generating function (m.g.f):

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

where β(x,y)\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)


[Package distributional version 0.4.0 Index]