# parlap: Estimate the Parameters of the Laplace Distribution

### Description

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 λ_1, λ_2, λ_3, and λ_4. The mathematical expressions are

ξ = λ_1 - 50/31\timesλ_3 \mbox{and}

α = 1.4741λ_2 - 0.5960λ_4 \mbox{.}

The alternative and even simpler method only uses λ_1 and λ_2. The mathematical expressions are

ξ = λ_1\mbox{\, and}

α = \frac{4}{3}λ_2\mbox{.}

The user could easily estimate the parameters from the L-moments and use vec2par to create a parameter object.

### Usage

 1 parlap(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 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. ... Other arguments to pass.

### Value

An R list is returned.

 type The type of distribution: lap. para The parameters of the distribution. source The source of the parameters: “parlap”.

### Note

The decision to use only one of the two systems of equations for Laplace fitting is largely arbitrary, but it seems most fitting to use four L-moments instead of two.

W.H. Asquith

### References

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

### Examples

 1 2 lmr <- lmoms(rnorm(20)) parlap(lmr) 

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