distributional (version 0.6.0)

dist_uniform: The Uniform distribution

Description

A distribution with constant density on an interval.

Usage

dist_uniform(min, max)

Arguments

min, max

lower and upper limits of the distribution. Must be finite.

Details

We recommend reading this documentation on pkgdown which renders math nicely. https://pkg.mitchelloharawild.com/distributional/reference/dist_uniform.html

In the following, let \(X\) be a Uniform random variable with parameters min = \(a\) and max = \(b\).

Support: \([a, b]\)

Mean: \(\frac{a + b}{2}\)

Variance: \(\frac{(b - a)^2}{12}\)

Probability density function (p.d.f):

$$ f(x) = \frac{1}{b - a} $$

for \(x \in [a, b]\), and \(f(x) = 0\) otherwise.

Cumulative distribution function (c.d.f):

$$ F(x) = \frac{x - a}{b - a} $$

for \(x \in [a, b]\), with \(F(x) = 0\) for \(x < a\) and \(F(x) = 1\) for \(x > b\).

Moment generating function (m.g.f):

$$ E(e^{tX}) = \frac{e^{tb} - e^{ta}}{t(b - a)} $$

for \(t \neq 0\), and \(E(e^{tX}) = 1\) for \(t = 0\).

Skewness: \(0\)

Excess Kurtosis: \(-\frac{6}{5}\)

See Also

stats::Uniform

Examples

dist <- dist_uniform(min = c(3, -2), max = c(5, 4))

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)