theoLmoms.max.ostat: Compute the Theoretical L-moments of a Distribution Distribution based on System of Maximum Order Statistic Expectations

Description

This function computes

Usage

theoLmoms.max.ostat(para=NULL, cdf=NULL, pdf=NULL, nmom=4, ...)

Arguments

para

A distribution parameter list from a function such as vec2par or lmom2par.

cdf

CDF of the distribution for the parameters.

pdf

PDF of the distribution for the parameters.

nmom

The number of L-moments to compute.

...

Optional, but likely, arguments to pass to expect.max.ostat. Such arguments will likely tailor the integrations limits specific for the distribution in question.

Value

An R list is returned.
lambdasVector of the L-moments. First element is $\lambda_1$, second element is $\lambda_2$, and so on.
ratiosVector of the L-moment ratios. Second element is $\tau$, third element is $\tau_3$ and so on.
trimLevel of symmetrical trimming used in the computation, which will equal NULL until trimming support is made.
leftrimLevel of left-tail trimming used in the computation, which will equal NULL until trimming support is made.
rightrimLevel of right-tail trimming used in the computation, which will equal NULL until trimming support is made.
sourceAn attribute identifying the computational source of the L-moments: theoLmoms.max.ostat.

Examples

Run this code

para <- vec2par(c(40,20), type='nor')
theoLmoms.max.ostat(para=para, cdf=cdfnor, pdf=pdfnor)

# The Rice distribution is complex and tailoring of the integration
# limits is needed to effectively trapped errors, the limits for the
# Normal distribution above are infinite so no granular control is needed.
para <- vec2par(c(30,10), type="rice")
theoLmoms.max.ostat(para=para, cdf=cdfrice, pdf=pdfrice,
                    lower=0, upper=.Machine$double.max)

# The Normal distribution is used on the fly for the Rice for
# high signal to noise ratios (SNR=nu/alpha > some threshold). This
# application here will error out.
nu <- 30; alpha <- 0.5
para <- vec2par(c(nu,alpha), type="rice")
theoLmoms.max.ostat(para=para, cdf=cdfrice, pdf=pdfrice,
                    lower=0, upper=.Machine$double.max)

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