actuar (version 3.3-4)

UniformSupp: 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)

Value

munif gives the \(k\)th raw moment,

levunif gives the \(k\)th 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.

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.

Author

Vincent Goulet , Christophe Dutang

Details

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

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)