Logistic: Create a Logistic distribution

In distributions3: Probability Distributions as S3 Objects

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)

distributions3 documentation built on Sept. 30, 2024, 9:37 a.m.