This function estimates the parameters of the Gamma Difference distribution given the L-moments of the data in an ordinary L-moment object (lmoms). The relations between distribution parameters and L-moments are complex (see lmomgdd). The distribution has four parameters. The vector para in the parameter object with a fifth parameter uses that as a trigger between a symmetrical distribution with para[3:4] equals para[1:2] if para[5] = 1. If para[5] is not present, then the distribution can be asymmetrical, or if para[5] is present and set to any value that is not 1, then the distribution can be asymmetrical.
pargdd(lmom, checklmom=TRUE, symgdd=FALSE, init.para=NULL, snap.tau4=FALSE,
silent=FALSE, trace=FALSE, control=list(abstol=0.0001, maxit=1000), ...)An R
list is returned.
The type of distribution: gdd.
The parameters of the distribution.
The source of the parameters: “pargdd”.
The results of the parameter optimization call.
An L-moment object created by lmoms or vec2lmom.
Should the lmom be checked for validity using the are.lmom.valid function.
A logical to trigger a symmetrical distribution by \(\alpha_2 = \alpha_1\) and \(\beta_1 = \beta_1\) and the fifth element of para on the return will be set to 1.
Optional initial values for the parameters used for starting values for the optim function. If this argument is not set, then an unrigorous attempt is made to guess at the initial parameters using some poor admittedly heuristics. The fifth element, if present, and set to 1, then the symdd is internally set to true.
A logical to trigger snapping \(\tau_4\) to a nudge above the \(\{\tau_3, \tau_4\}\) trajectory of the Pearson Type III distribution. The Gamma Difference only has solution in \(\{\tau_3, \tau_4\}\) domain above the Pearson.
The argument silent for try().
A logical to trigger a message in the main objective function.
The argument control for optim().
Other arguments to pass.
W.H. Asquith
lmomgdd, cdfgdd, pdfgdd, quagdd