distributional (version 0.5.0)

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 https://pkg.mitchelloharawild.com/distributional/, where the math will render nicely.

In the following, let \(X\) be a Poisson random variable with parameter lambda = \(\lambda\).

Support: \([a,b]\)

Mean: \(\frac{1}{2}(a+b)\)

Variance: \(\frac{1}{12}(b-a)^2\)

Probability mass function (p.m.f):

$$ f(x) = \frac{1}{b-a} for x \in [a,b] $$ $$ f(x) = 0 otherwise $$

Cumulative distribution function (c.d.f):

$$ F(x) = 0 for x < a $$ $$ F(x) = \frac{x - a}{b-a} for x \in [a,b] $$ $$ F(x) = 1 for x > b $$

Moment generating function (m.g.f):

$$ E(e^{tX}) = \frac{e^{tb} - e^{ta}}{t(b-a)} for t \neq 0 $$ $$ E(e^{tX}) = 1 for t = 0 $$

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)