partri {lmomco} | R Documentation |
Estimate the Parameters of the Asymmetric Triangular Distribution
Description
This function estimates the parameters of the Asymmetric Triangular distribution given the L-moments of the data in an L-moment object such as that returned by lmoms
. The relations between distribution parameters and L-moments are seen under lmomtri
.
The estimtion by the partri
function is built around simultaneous numerical optimization of an objective function defined as
for estimation of the three parameters (, minimum;
, mode; and
, maximum) from the sample L-moments (
,
,
). The divisions shown in the objective function are used for scale removal to help make each L-moment order somewhat similar in its relative contribution to the solution. The coefficient of L-variation is not used because the distribution implementation by the lmomco package supports entire real number line and the loss of definition of
at
, in particular, causes untidiness in coding.
The function is designed to support both left- or right-hand right triangular shapes because of (1) paracheck
argument availability in lmomtri
, (2) the sorting of the numerical estimates if the mode is no compatable with either of the limits, and (3) the snapping of when
or
when
where the
versions are the optimized values if the
is very near to its numerical bounds.
Usage
partri(lmom, checklmom=TRUE, ...)
Arguments
lmom |
|
checklmom |
Should the |
... |
Other arguments to pass. |
Value
An R list
is returned.
type |
The type of distribution: |
para |
The parameters of the distribution. |
obj.val |
The value of the objective function, which is the error of the optimization. |
source |
The source of the parameters: “partri”. |
Author(s)
W.H. Asquith
See Also
lmomtri
,
cdftri
, pdftri
, quatri
Examples
lmr <- lmomtri(vec2par(c(10,90,100), type="tri"))
partri(lmr)
partri(lmomtri(vec2par(c(-11, 67,67), type="tri")))$para
partri(lmomtri(vec2par(c(-11,-11,67), type="tri")))$para