This function estimates the parameters of the Laplace 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 sample L-moments are simple, but there are two methods. The first method, which is the only one implemented in lmomco, jointly uses \(\lambda_1, \lambda_2, \lambda_3\), and \(\lambda_4\). The mathematical expressions are
$$\xi = \lambda_1 - 50/31\times\lambda_3 \mbox{and}$$
$$\alpha = 1.4741\lambda_2 - 0.5960\lambda_4 \mbox{.}$$
The alternative and even simpler method only uses \(\lambda_1\) and \(\lambda_2\). The mathematical expressions are
$$\xi = \lambda_1\mbox{\, and}$$
$$\alpha = \frac{4}{3}\lambda_2\mbox{.}$$
The user could easily estimate the parameters from the L-moments and use vec2par to create a parameter object.
parlap(lmom, checklmom=TRUE, ...)An R
list is returned.
The type of distribution: lap.
The parameters of the distribution.
The source of the parameters: “parlap”.
An L-moment object created by lmoms or vec2lmom.
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 \(\tau_4\) and \(\tau_3\) inequality). However, for some circumstances or large simulation exercises then one might want to bypass this check.
Other arguments to pass.
W.H. Asquith
Hosking, J.R.M., 1986, The theory of probability weighted moments: IBM Research Report RC12210, T.J. Watson Research Center, Yorktown Heights, New York.
lmomlap,
cdflap, pdflap, qualap
lmr <- lmoms(rnorm(20))
parlap(lmr)
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