Stable lifecycle

dist_logistic(location, scale)

Arguments

location

location and scale parameters.

scale

location and scale parameters.

Details

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.

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
#> <distribution[5]> #> [1] Logistic(5, 2) Logistic(9, 3) Logistic(9, 4) Logistic(6, 2) Logistic(2, 1)
mean(dist)
#> [1] 5 9 9 6 2
variance(dist)
#> [1] 13.159473 29.608813 52.637890 13.159473 3.289868
skewness(dist)
#> [1] 0 0 0 0 0
kurtosis(dist)
#> [1] 1.2 1.2 1.2 1.2 1.2
generate(dist, 10)
#> [[1]] #> [1] 3.051111 4.443118 4.328958 1.273285 6.566140 1.858059 9.981575 5.926152 #> [9] 3.452139 7.896554 #> #> [[2]] #> [1] 15.671659 3.170429 9.791241 3.234065 10.565773 1.477064 6.247261 #> [8] 6.608087 3.718496 13.154582 #> #> [[3]] #> [1] 2.713815 14.196408 8.519997 7.920825 10.201478 12.977880 17.536972 #> [8] 3.944472 5.449427 14.875827 #> #> [[4]] #> [1] -0.1761264 6.0421749 3.7127549 6.7208426 13.0320687 3.6139797 #> [7] 9.7566396 1.8340325 8.7912884 7.3081170 #> #> [[5]] #> [1] 2.6280814 0.7708067 3.7661612 1.7409898 1.1011250 2.5648962 0.9774935 #> [8] 1.5369747 2.4861284 2.1671001 #>
density(dist, 2)
#> [1] 0.07457323 0.02686172 0.03153231 0.05249679 0.25000000
density(dist, 2, log = TRUE)
#> [1] -2.595974 -3.617053 -3.456743 -2.947003 -1.386294
cdf(dist, 4)
#> [1] 0.3775407 0.1588691 0.2227001 0.2689414 0.8807971
quantile(dist, 0.7)
#> [1] 6.694596 11.541894 12.389191 7.694596 2.847298