Description Usage Arguments Value Author(s) References See Also Examples
This function estimates the Lmoments of the Laplace distribution given the parameters (ξ and α) from parlap
. The Lmoments in terms of the parameters are
λ_1 = ξ,
λ_2 = 3α/4,
τ_3 = 0,
τ_4 = 17/22,
τ_5 = 0, and
τ_6 = 31/360.
For r odd and r ≥ 3, λ_r = 0, and for r even and r ≥ 4, the Lmoments using the hypergeometric function {}_2F_1() are
λ_r = \frac{2α}{r(r1)}[1  {}_2F_1(r, r1, 1, 1/2)]\mbox{,}
where {}_2F_1(a, b, c, z) is defined as
{}_2F_1(a, b, c, z) = ∑_{n=0}^∞ \frac{(a)_n(b)_n}{(c)_n}\frac{z^n}{n!}\mbox{,}
where (x)_n is the rising Pochhammer symbol, which is defined by
(x)_n = 1 \mbox{\ for\ } n = 0\mbox{, and}
(x)_n = x(x+1)\cdots(x+n1) \mbox{\ for\ } n > 0\mbox{.}
1  lmomlap(para)

para 
The parameters of the distribution. 
An R list
is returned.
lambdas 
Vector of the Lmoments. First element is λ_1, second element is λ_2, and so on. 
ratios 
Vector of the Lmoment ratios. Second element is τ, third element is τ_3 and so on. 
trim 
Level of symmetrical trimming used in the computation, which is 
leftrim 
Level of lefttail trimming used in the computation, which is 
rightrim 
Level of righttail trimming used in the computation, which is 
source 
An attribute identifying the computational source of the Lmoments: “lmomlap”. 
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.
parlap
, cdflap
, pdflap
, qualap
1 2 3 
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