theopwms | R Documentation |
Compute the theoretrical probability-weighted moments (PWMs) for a distribution. A theoretrical PWM in integral form is
\beta_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, which is a parameter object of lmomco (see vec2par
).
theopwms(para, nmom=5, verbose=FALSE)
para |
A distribution parameter object such as that by |
nmom |
The number of moments to compute. Default is 5. |
verbose |
Toggle verbose output. Because the R function |
An R list
is returned.
betas |
The PWMs. Note that convention is the have a |
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, v. 52, p. 105–124.
theoLmoms
, pwm
, pwm2lmom
para <- vec2par(c(0,1),type='nor') # standard normal
the.pwms <- theopwms(para) # compute PWMs
str(the.pwms)
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