# parkap: Estimate the Parameters of the Kappa Distribution In lmomco: L-Moments, Censored L-Moments, Trimmed L-Moments, L-Comoments, and Many Distributions

## Description

This function estimates the parameters of the Kappa distribution given the L-moments of the data in an L-moment object such as that returned by lmoms. The relations between distribution parameters and L-moments are seen under lmomkap, but of relevance to this documentation, the upper bounds of L-kurtosis (τ_4) and a function of L-skew (τ_3) is given by

τ_4 < \frac{5τ_3^2+1}{6}

This bounds is equal to the Generalized Logistic distribution (parglo) and failure occurs if this upper bounds is exceeded. However, the argument snap.tau4, if set, will set τ_4 equal to the upper bounds of τ_4 of the distribution to the relation above. This value of τ_4 should be close enough numerically The argument nudge.tau4 is provided to offset τ_4 downward just a little. This keeps the relation operator as “<” in the bounds above to match Hosking's tradition as his sources declare “” as above the GLO. The nudge here hence is not zero, which is a little different compared to the conceptually similar snapping in paraep4.

## Usage

 1 2 parkap(lmom, checklmom=TRUE, snap.tau4=FALSE, nudge.tau4=sqrt(.Machine$double.eps), ...)  ## Arguments  lmom An L-moment object created by lmoms or vec2lmom. checklmom Should the lmom be checked for validity using the are.lmom.valid function. Normally this should be left as the default and it is very unlikely that the L-moments will not be viable (particularly in the τ_4 and τ_3 inequality). However, for some circumstances or large simulation exercises then one might want to bypass this check. snap.tau4 A logical to “snap” the τ_4 downwards to the lower boundary if the given τ_4 is greater than the boundary described as above. nudge.tau4 An offset to the snapping of τ_4 intended to move τ_4 just below the upper bounds. (The absolute value of the nudge is made internally to ensure only downward adjustment by a subtraction operation.) ... Other arguments to pass. ## Value An R list is returned.  type The type of distribution: kap. para The parameters of the distribution. source The source of the parameters: “parkap”. support The support (or range) of the fitted distribution. ifail A numeric failure code. ifailtext A text message for the failure code. ## Author(s) W.H. Asquith ## References Hosking, J.R.M., 1994, The four-parameter kappa distribution: IBM Journal of Reserach and Development, v. 38, no. 3, pp. 251–258. Hosking, J.R.M., and Wallis, J.R., 1997, Regional frequency analysis—An approach based on L-moments: Cambridge University Press. ## See Also lmomkap, cdfkap, pdfkap, quakap ## Examples  1 2 3 4 5 6 lmr <- lmoms(rnorm(20)) parkap(lmr) ## Not run: parkap(vec2lmom(c(0,1,.3,.8)), snap.tau4=TRUE) # Tau=0.8 is way above the GLO. ## End(Not run)  ### Example output $type
[1] "kap"

$para xi alpha kappa h -0.03276148 1.26628252 0.94534247 0.10277668$source
[1] "parkap"

$support lower upper -10.202315 1.306735$ifail
[1] 0

$ifailtext [1] "Successful parameter estimation."$type
[1] "kap"

$para xi alpha kappa h 0 0 0 0$source
[1] "parkap"

$support [1] NA NA$ifail
[1] 2

\$ifailtext
[1] "TAU3 and TAU4 are above Generalized Logistic line."


lmomco documentation built on Sept. 21, 2018, 6:40 p.m.