Description Usage Arguments Details Value Examples
Raw moments for the Weibull distribution.
1 |
r |
rth raw moment of the distribution, defaults to 1. |
truncation |
lower truncation parameter, defaults to 0. |
shape, scale |
shape and scale of the distribution with default values of 2 and 1 respectively. |
lower.tail |
logical; if TRUE (default), moments are E[x^r|X ≤ y], otherwise, E[x^r|X > y] |
Probability and Cumulative Distribution Function:
f(x) = \frac{shape}{scale}(\frac{ω}{scale})^{shape-1}e^{-(\frac{ω}{scale})^shape} , \qquad F_X(x) = 1-e^{-(\frac{ω}{scale})^shape}
The y-bounded r-th raw moment of the distribution equals:
μ^r_y = scale^{r} Γ(\frac{r}{shape} +1, (\frac{y}{scale})^shape )
where Γ(,) denotes the upper incomplete gamma function.
returns the truncated rth raw moment of the distribution.
1 2 3 4 5 6 7 8 9 10 11 12 | ## The zeroth truncated moment is equivalent to the probability function
pweibull(2, shape = 2, scale = 1)
mweibull(truncation = 2)
## The (truncated) first moment is equivalent to the mean of a (truncated) random sample,
#for large enough samples.
x <- rweibull(1e5, shape = 2, scale = 1)
mean(x)
mweibull(r = 1, lower.tail = FALSE)
sum(x[x > quantile(x, 0.1)]) / length(x)
mweibull(r = 1, truncation = quantile(x, 0.1), lower.tail = FALSE)
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