UniformSupp: Moments and Moment Generating Function of the Uniform...

In actuar: Actuarial Functions and Heavy Tailed Distributions

Moments and Moment Generating Function of the Uniform Distribution

Description

Raw moments, limited moments and moment generating function for the Uniform distribution from min to max.

Usage

munif(order, min = 0, max = 1)
levunif(limit, min = 0, max =1, order = 1)
mgfunif(t, min = 0, max = 1, log = FALSE)

Arguments

order	order of the moment.
min, max	lower and upper limits of the distribution. Must be finite.
limit	limit of the random variable.
t	numeric vector.
log	logical; if TRUE, the cumulant generating function is returned.

Details

The kth raw moment of the random variable X is E[X^k], the kth limited moment at some limit d is E[\min(X, d)^k] and the moment generating function is E[e^{tX}].

Value

munif gives the kth raw moment, levunif gives the kth moment of the limited random variable, and mgfunif gives the moment generating function in t.

Invalid arguments will result in return value NaN, with a warning.

Author(s)

Vincent Goulet [e-mail], Christophe Dutang

References

https://en.wikipedia.org/wiki/Uniform_distribution_%28continuous%29

See Also

Uniform.

Examples

munif(-1)
munif(1:5)
levunif(3, order=1:5)
levunif(3, 2, 4)
mgfunif(1, 1, 2)

actuar documentation built on Aug. 9, 2025, 1:06 a.m.