This function estimates the trimmed L-moments of the Slash distribution given the parameters (\(\xi\) and \(\alpha\)) from parsla. The relation between the TL-moments (trim=1) and the parameters have been numerically determined and are
\(\lambda^{(1)}_1 = \xi\),
\(\lambda^{(1)}_2 = 0.93686275\alpha\),
\(\tau^{(1)}_3 = 0\),
\(\tau^{(1)}_4 = 0.30420472\),
\(\tau^{(1)}_5 = 0\), and
\(\tau^{(1)}_6 = 0.18900723\).
These TL-moments (trim=1) are symmetrical for the first L-moments defined because \(\mathrm{E}[X_{1:n}]\) and \(\mathrm{E}[X_{n:n}]\) are undefined expectations for the Slash.
lmomsla(para)An R
list is returned.
Vector of the trimmed L-moments. First element is \(\lambda^{(1)}_1\), second element is \(\lambda^{(1)}_2\), and so on.
Vector of the L-moment ratios. Second element is \(\tau^{(1)}\), third element is \(\tau^{(1)}_3\) and so on.
Level of symmetrical trimming used in the computation, which is 1.
Level of left-tail trimming used in the computation, which is 1.
Level of right-tail trimming used in the computation, which is 1.
An attribute identifying the computational source of the L-moments: “lmomsla”
Level of symmetrical trimming used.
The parameters of the distribution.
W.H. Asquith
Rogers, W.H., and Tukey, J.W., 1972, Understanding some long-tailed symmetrical distributions: Statistica Neerlandica, v. 26, no. 3, pp. 211--226.
parsla, cdfsla, pdfsla, quasla