theopwms {lmomco} | R Documentation |
Compute the theoretrical probability-weighted moments (PWMs) for a distribution. A theoretrical PWM in integral form is
β_r = int^1_0 X(F),F^r,mathrm{d}F mbox{,}
where X(F) is the quantile function of the random variable X for nonexceedance probability F and r represents the order of the PWM. This function loops across the above equation for each nmom
set in the argument list. The function X(F) is computed through the par2qua
function. The distribution type is determined using the type
attribute of the para
argument—the parameter object.
theopwms(para,nmom=5,verbose=FALSE)
para |
A distribution parameter object of this package vec2par . |
nmom |
The number of moments to compute. Default is 5. |
verbose |
Toggle verbose output. Because the R function integrate is used to perform the numerical integration, it might be useful to see selected messages regarding the numerical integration. |
An R list
is returned.
betas |
The PWMs. Note that convention is the have a β_0, but this is placed in the first index i=1 of the betas vector. |
source |
An attribute identifying the computational source of the probability-weighted moments: “theopwms”. |
W.H. Asquith
Hosking, J.R.M., 1990, L-moments–Analysis and estimation of distributions using linear combinations of order statistics: Journal of the Royal Statistical Society, Series B, vol. 52, p. 105-124.
para <- vec2par(c(0,1),type='nor') # standard normal the.pwms <- theopwms(para) # compute PWMs str(the.pwms)