dist_uniform(min, max)
lower and upper limits of the distribution. Must be finite.
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):
$$ E(e^{tX}) = \frac{e^{tb} - e^{ta}}{t(b-a)} for t \neq 0 $$ $$ E(e^{tX}) = 1 for t = 0 $$
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] 3.853052 3.101802 3.011493 3.763697 4.989991 3.282418 3.707240 4.007333
#> [9] 3.946254 4.329282
#>
#> [[2]]
#> [1] 1.4899095 3.7600330 1.3168641 3.9419258 0.6191111 0.8674027
#> [7] -0.4445284 -1.3764096 -0.4060009 -1.8360372
#>
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