This function estimates the L-moments of the Gamma Difference distribution (Klar, 2015) given the parameters (\(\alpha_1 > 0\), \(\beta_1 > 0\), \(\alpha_2 > 0\), \(\beta_2 > 0\)) from pargdd. The L-moments in terms of the parameters higher than the mean are complex and numerical methods are required. The mean is
$$\lambda_1 = \frac{\alpha_1}{\beta_1} - \frac{\alpha_2}{\beta_2} \mbox{.}$$
The product moments, however, have simple expressions, the variance and skewness, respectively are
$$\sigma^2 = \frac{\alpha_1}{\beta_2^2} + \frac{\alpha_2}{\beta_2^2}\mbox{,}$$
and
$$\gamma = \frac{2\bigl(\alpha_1{\beta_2^3} + \alpha_2{\beta_2^2}\bigr)} {\bigl(\alpha_2{\beta_1^2} + \alpha_2{\beta_1^2}\bigr)^{3/2}}\mbox{.}$$
lmomgdd(para, nmom=6, paracheck=TRUE, silent=TRUE, ...)An R
list is returned.
Vector of the L-moments. First element is \(\lambda_1\), second element is \(\lambda_2\), and so on.
Vector of the L-moment ratios. Second element is \(\tau\), third element is \(\tau_3\) and so on.
Level of symmetrical trimming used in the computation, which is 0.
Level of left-tail trimming used in the computation, which is NULL.
Level of right-tail trimming used in the computation, which is NULL.
An attribute identifying the computational source of the L-moments: “lmomgdd”.
The parameters of the distribution.
The number of L-moment to numerically compute for the distribution.
A logical controlling whether the parameters are checked for validity.
The argument of silent for the try() operation wrapped on integrate().
Additional argument to pass.
W.H. Asquith
pargdd, cdfgdd, pdfgdd, quagdd