weibull function

The Weibull distribution

Raw moments for the Weibull distribution.

mweibull(r = 0, truncation = 0, shape = 2, scale = 1, lower.tail = TRUE)

Arguments

• 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 $E[x^r|X \le y]$, otherwise, $E[x^r|X > y]$

Returns

returns the truncated rth raw moment of the distribution.

Details

Probability and Cumulative Distribution Function:

The y-bounded r-th raw moment of the distribution equals:

where $\Gamma(,)$ denotes the upper incomplete gamma function.

Examples

## 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)