parsmd {lmomco}

Estimate the Parameters of the Singh–Maddala Distribution

Description

This function estimates the parameters of the Singh–Maddala (Burr Type XII) distribution given the L-moments of the data in an L-moment object such as that returned by lmoms. The L-moments in terms of the parameters are complicated and solved numerically. Extensive study of the computational limits of the R implementation are incorporated within the source code of the function. The file lmomco/inst/doc/domain_of_smd.R contains the algorithmic sweep used to compute the L-skew and L-kurtosis attainable domain of the distribution.

Usage

parsmd(lmom, checklmom=TRUE, checkbounds=TRUE, snap.tau4=TRUE, ...)

Arguments

lmom

An L-moment object created by lmoms or vec2lmom.

checklmom

Should the lmom be checked for validity using the are.lmom.valid function. Normally this should be left as the default and it is very unlikely that the L-moments will not be viable (particularly in the \tau_3 and \tau_4 inequality,
are.lmom.valid). However, for some circumstances or large simulation exercises then one might want to bypass this check.

checkbounds

Should the lower bounds of \tau_4 be verified and if sample \hat\tau_3 and \hat\tau_4 are outside of these bounds, then NA are returned for the solutions.

snap.tau4

A logical to trigger the application of the empirical limits of the distribution in terms of \tau_3 and \tau_4 wherein parameter estimation appears numerically possible and such parameters return the given values of these L-moment ratios. The lower and upper limits of \tau_4 are defined by separate polynomials as functions of \tau_3. If the logical is true, then \tau_4 in excess of the upper bounds are assigned to the upper bounds and \tau_4 in deficit of the lower bounds are assigned to the lower bounds. Messages within the returned parameter object are provided if the snapping occurs.

...

Other arguments to pass.

Value

An R list is returned.

type

The type of distribution: smd.

para

The parameters of the distribution.

last_para

The last or final iteration of the parameters that are the same as para if ifail is zero. This provides a way to preserve where the parameter left off or gave up.

source

The source of the parameters: “parsmd”.

iter

The number of iteration attempts looping on the optim() call.

rt

The output of the optim() call.

message

A message from parsmd, which generally involves checkbounds=TRUE and
snap.tau4=TRUE on the resetting or snapping of the \tau_3 and \tau_4 to the computational bounds for the distribution.

ifail

A interger flag to status of the operations: -1 means that the L-moments are invalid (if they are checked), 0 means that the parameter estimation appears successful, and 1 means that the parameter estimation appears to have failed.

Author(s)

W.H. Asquith

References

Shahzad, M.N., and Zahid, A., 2013, Parameter estimation of Singh Maddala distribution by moments: International Journal of Advanced Statistics and Probability, v. 1, no. 3, pp. 121–131, doi:10.14419/ijasp.v1i3.1206.

See Also

lmomsmd, cdfsmd, pdfsmd, quasmd

Examples

lmr <- lmoms(rnorm(20))
parsmd(lmr, snap.tau4=TRUE)