parpdq3 {lmomco}

Estimate the Parameters of the Polynomial Density-Quantile3 Distribution

Description

This function estimates the parameters of the Polynomial Density-Quantile3 distribution given the L-moments of the data in an L-moment object such as that returned by lmoms. The relations between the distribution parameters and L-moments are seen under lmompdq3.

Usage

parpdq3(lmom, checklmom=TRUE)

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 unlikely that the L-moments will not be viable. However, for some circumstances or large simulation exercises then one might want to bypass this check.

Value

An R list is returned.

type

The type of distribution: pdq3.

para

The parameters of the distribution.

ifail

A numeric field connected to the ifailtext; a value of 0 indicates fully successful operation of the function.

ifailtext

A message, instead of a warning, about the internal operations or operational limits of the function.

source

The source of the parameters: “parpdq3”.

Note

The following is a study of the performance of parpdq3 as the upper limit of the shape parameter \kappa is approached. The algorithms have the ability to estimate the \kappa reliabily, it is the scale parameter \alpha that breaks down and hence there is a hard-wired setting of |\kappa| > 0.98 in which a warning is issue in parpdq3 about \alpha reliability:

  A <- 10
  K <- seq(0.8, 1, by=0.0001)
  K <- sort(c(-K, K))
  As <- Ks <- rep(NA, length(K))
  for(i in 1:length(K)) {
    para <- list(para=c(0, A, K[i]), type="pdq3")
    As[i] <- parpdq3( lmompdq3(para) )$para[2]
    Ks[i] <- parpdq3( lmompdq3(para) )$para[3]
  }
  plot( K, (As-A)/A, type="l", col="red")
  abline(v=c(-0.98, +0.98)) # heuristically determined threshold

Author(s)

W.H. Asquith

References

Hosking, J.R.M., 2007, Distributions with maximum entropy subject to constraints on their L-moments or expected order statistics: Journal of Statistical Planning and Inference, v. 137, no. 9, pp. 2870–2891, doi:10.1016/j.jspi.2006.10.010.

See Also

lmompdq3, cdfpdq3, pdfpdq3, quapdq3

Examples

para <- list(para=c(0, 0.4332, -0.7029), type="pdq3")
parpdq3(lmompdq3(para))$para

para <- list(para=c(0, 0.4332, 0.7029), type="pdq3")
parpdq3(lmompdq3(para))$para

para <- list(para=c(0, 0.4332, 1-sqrt(.Machine$double.eps)), type="pdq3")
parpdq3(lmompdq3(para))$para

para <- list(para=c(0, 0.4332, -1+sqrt(.Machine$double.eps)), type="pdq3")
parpdq3(lmompdq3(para))$para

para <- list(para=c(0, 0.4332, +0.0001), type="pdq3")
parpdq3(lmompdq3(para))$para

para <- list(para=c(0, 0.4332, -0.0001), type="pdq3")
parpdq3(lmompdq3(para))$para

para <- list(para=c(0, 0.4332, 0), type="pdq3")
parpdq3(lmompdq3(para))$para