Stable lifecycle

dist_uniform(min, max)

Arguments

min

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

max

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

Details

A distribution with constant density on an interval.

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

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] 3.719182 4.310035 3.208588 4.820395 3.247009 3.970001 3.848841 4.413332 #> [9] 3.614408 4.918179 #> #> [[2]] #> [1] -0.08341130 0.23677863 3.05051087 -0.03648231 3.39143916 1.96795113 #> [7] 2.38681148 -1.41493439 -0.04912791 2.51548383 #>
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