lmomco (version 1.3.3)

lmom.diff: Difference Between L-moments of the Distribution and the L-moments of the Data

Description

This function computes the difference between the L-moments derived from a parameterized distribution and the L-moments as computed from the data. This function is useful to characterize the bias that develops between the theoretical L-moments of a distribution and the L-moments of the data. This function also is an important test on the algorithms that fit distributions to the L-moments. The difference is computed as the L-moment from the distribution minus the L-moment of the data. The lmorph function is used internally to get the L-moment objects into the appropriate format.

Usage

lmom.diff(lmomparm, lmomdata, verbose=TRUE, digits=4)

Arguments

lmomparm

L-moments of a distribution such as from par2lmom

lmomdata

L-moments of the data such as from lmom.ub

verbose

Logical switch on verbosity of output. Default is TRUE.

digits

Number of digits to pass internally to the signif function for rounding of results.

Value

• "THE FIVE DIFFERENCES BETWEEN L-MOMENTS OF DISTRIBUTION AND DATA"

  L1diff L2diff T3diff T4diff T5diff

  1 0 -1.11e-16 -0.7345 -0.4005 -0.3942

  where the five values are the differences between the theoretical L-moments of the fitted distribution and the sample L-moments of the data (theoretical minus sample) in the titled column. These values are also returned as part of an R list. If a list element has numeric(0) then likely one of the L-moments is NULL or NA for the distribution such as the results reported for the example involving the Generalized Logistic distribution (glo).

  A dataframe of the difference is the returned value.

See Also

par2lmom, lmom2par, lmorph

Examples

# The first three moment differences are zero because the GLO is only 
  # fit to these and not the higher moments.
  lmr <- lmom.ub(rnorm(40))
  para <- lmom2par(lmr, type = 'glo')
  lmom.diff(par2lmom(para),lmr)

  # The first two moment differences are zero because the Normal is only 
  # fit to these and not the higher moments.
  lmr <- lmom.ub(rnorm(40))
  lmr <- lmorph(lmr)
  para <- parnor(lmr)
  lmom.diff(lmomnor(para),lmr)