dist_logistic {distributional} | R Documentation |
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
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)