Create a Logistic distribution
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.
Logistic(location = 0, scale = 1)
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. |
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 = 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.
A Logistic object.
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)
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