| Logistic {distributions3} | 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 \beta) 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 = \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.
Value
A Logistic object.
See Also
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)