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)
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.
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.
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 \(E[e^{tX}]\).