lmomTLgpa: Trimmed L-moments of the Generalized Pareto Distribution
Description
This function estimates the symmetrical trimmed L-moments (TL-moments) for \(t=1\) of the Generalized Pareto distribution given the parameters (\(\xi\), \(\alpha\), and \(\kappa\)) from parTLgpa.
The TL-moments in terms of the parameters are
$$\lambda^{(1)}_1 = \xi + \frac{\alpha(\kappa+5)}{(\kappa+3)(\kappa+2)} \mbox{,}$$
$$\lambda^{(1)}_2 = \frac{6\alpha}{(\kappa+4)(\kappa+3)(\kappa+2)} \mbox{,}$$
$$\tau^{(1)}_3 = \frac{10(1-\kappa)}{9(\kappa+5)} \mbox{, and}$$
$$\tau^{(1)}_4 = \frac{5(\kappa-1)(\kappa-2)}{4(\kappa+6)(\kappa+5)} \mbox{.}$$
Usage
lmomTLgpa(para)
Value
An R
list is returned.
lambdas
Vector of the trimmed L-moments. First element is
\(\lambda^{(1)}_1\), second element is \(\lambda^{(1)}_2\), and so on.
ratios
Vector of the L-moment ratios. Second element is
\(\tau^{(1)}\), third element is \(\tau^{(1)}_3\) and so on.
trim
Level of symmetrical trimming used in the computation, which is unity.
leftrim
Level of left-tail trimming used in the computation, which is unity.
rightrim
Level of right-tail trimming used in the computation, which is unity.
source
An attribute identifying the computational source of the TL-moments: “lmomTLgpa”.
Arguments
para
The parameters of the distribution.
Author
W.H. Asquith
References
Elamir, E.A.H., and Seheult, A.H., 2003, Trimmed L-moments: Computational Statistics and Data Analysis, v. 43, pp. 299--314.