The Uniform distribution

A distribution with constant density on an interval.

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: $-\frac{6}{5}$

Examples

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

dist
#> <distribution[2]>
#> [1] U(3, 5)  U(-2, 4)
mean(dist)
#> [1] 4 1
variance(dist)
#> [1] 0.3333333 3.0000000
skewness(dist)
#> [1] 0 0
kurtosis(dist)
#> [1] -1.2 -1.2

generate(dist, 10)
#> [[1]]
#>  [1] 4.223428 4.589334 3.587663 4.997371 4.120626 4.736963 4.300097 3.004776
#>  [9] 4.916369 4.894184
#> 
#> [[2]]
#>  [1]  3.92456879  2.17786698  3.85857148  2.15466275  3.82936825 -0.61351421
#>  [7]  1.32545154 -1.19708572 -0.05658736  2.57998357
#> 

density(dist, 2)
#> [1] 0.0000000 0.1666667
density(dist, 2, log = TRUE)
#> [1]      -Inf -1.791759

cdf(dist, 4)
#> [1] 0.5 1.0

quantile(dist, 0.7)
#> [1] 4.4 2.2

Arguments

Details

See also

Examples