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lmomco (version 2.3.1)

lmomlap: L-moments of the Laplace Distribution

Description

This function estimates the L-moments of the Laplace distribution given the parameters (ξ and α) from parlap. The L-moments in terms of the parameters are λ1=ξ, λ2=3α/4, τ3=0, τ4=17/22, τ5=0, and τ6=31/360.

For r odd and r3, λr=0, and for r even and r4, the L-moments using the hypergeometric function 2F1() are λr=2αr(r1)[12F1(r,r1,1,1/2)], where 2F1(a,b,c,z) is defined as 2F1(a,b,c,z)=n=0(a)n(b)n(c)nznn!, where (x)n is the rising Pochhammer symbol, which is defined by (x)n=1\ for\ n=0, and (x)n=x(x+1)(x+n1)\ for\ n>0.

Usage

lmomlap(para)

Arguments

para

The parameters of the distribution.

Value

An R list is returned.

lambdas

Vector of the L-moments. First element is λ1, second element is λ2, and so on.

ratios

Vector of the L-moment ratios. Second element is τ, third element is τ3 and so on.

trim

Level of symmetrical trimming used in the computation, which is 0.

leftrim

Level of left-tail trimming used in the computation, which is NULL.

rightrim

Level of right-tail trimming used in the computation, which is NULL.

source

An attribute identifying the computational source of the L-moments: “lmomlap”.

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.

See Also

parlap, cdflap, pdflap, qualap

Examples

Run this code
# NOT RUN {
lmr <- lmoms(c(123,34,4,654,37,78))
lmr
lmomlap(parlap(lmr))
# }

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