lmomst3 {lmomco} | R Documentation |
L-moments of the 3-Parameter Student t Distribution
Description
This function estimates the first six L-moments of the 3-parameter Student t distribution given the parameters (,
,
) from
parst3
. The L-moments in terms of the parameters are
where is the cumulative distribution function of the Beta distribution. The distribution is symmetrical so that
for odd values of
.
Numerical integration of is made to estimate . The other two parameters are readily solved for when
is available. A polynomial approximation is used to estimate the
as a function of
; the polynomial was based on the
theoLmoms
estimating and
. The
polynomial has nine coefficients with a maximum absolute residual value of 2.065e-06 for 4,000 degrees of freedom (see
inst/doc/t4t6/studyST3.R
).
Usage
lmomst3(para, ...)
Arguments
para |
The parameters of the distribution. |
... |
Additional arguments to pass. |
Value
An R list
is returned.
lambdas |
Vector of the L-moments. First element is |
ratios |
Vector of the L-moment ratios. Second element is |
trim |
Level of symmetrical trimming used in the computation, which is |
leftrim |
Level of left-tail trimming used in the computation, which is |
rightrim |
Level of right-tail trimming used in the computation, which is |
source |
An attribute identifying the computational source of the L-moments: “lmomst3”. |
Author(s)
W.H. Asquith with A.R. Biessen
References
Asquith, W.H., 2011, Distributional analysis with L-moment statistics using the R environment for statistical computing: Createspace Independent Publishing Platform, ISBN 978–146350841–8.
See Also
parst3
, cdfst3
, pdfst3
, quast3
Examples
lmomst3(vec2par(c(1124, 12.123, 10), type="st3"))