theopwms: The Theoretical Probability-Weighted Moments using Integration of the Quantile Function

Description

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---the parameter object.

Usage

theopwms(para,nmom=5,verbose=FALSE)

Arguments

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.

Value

An R list is returned.
betasThe PWMs. Note that convention is the have a $\beta_0$, but this is placed in the first index i=1 of the betas vector.
sourceAn attribute identifying the computational source of the probability-weighted moments: theopwms.

References

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.

Examples

Run this code

para     <- vec2par(c(0,1),type='nor') # standard normal
the.pwms <- theopwms(para) # compute PWMs
str(the.pwms)

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