dist_uniform
The Uniform distribution
Description
![[Stable]](../help/figures/lifecycle-stable.svg)
Usage
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 = λ.
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 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)