MLEstimFct: Maximum likelihood (ML) method.

Description Usage Arguments Details Value References See Also Examples

Description

Uses the numerical ML approach described by Nolan to estimate the 4 parameters of stable law. The method may be slow for large sample size due to the use of numerical optimisation routine.

Usage

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MLParametersEstim(x, theta0 = NULL,
                  pm = 0, PrintTime = FALSE, ...)

Arguments

x

Data used to perform the estimation: vector of length n.

theta0

Initial guess for the 4 parameters values: If NULL, the Kogon-McCulloch method is called, see IGParametersEstim; a vector of length 4.

pm

Parametrisation, an integer (0 or 1); default: pm=0 (the Nolan ‘S0’ parametrisation).

PrintTime

Logical flag; if set to TRUE, the estimation duration is printed out to the screen in a readable format (h/min/sec).

...

Other argument to be passed to the optimisation function.

Details

The function performs the minimisation of the numerical (-)log-density of stable law computed by function dstable from the stabledist package. After testing several optimisation routines, we have found out that the "L-BFGS-B" algorithm performs better with the ML method (faster, more accurate).

Value

Returns a list with the following elements:

Estim

output of the optimisation function

duration

estimation duration in a numerical format

method

character describing the method used

References

Nolan J (2001). “Maximum likelihood estimation and diagnostics for stable distributions.” L'evy processes: theory and applications, pp. 379–400.

See Also

Estim

Examples

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theta <- c(1.5,0.4,1,0)
pm <- 0
## 50 points does not give accurate estimation
## but it makes estimation fast for installation purposes
## use at least 200 points to get decent results.
set.seed(1333);x <- rstable(50,theta[1],theta[2],theta[3],theta[4],pm)

## This example takes > 30 sec hence commented
##ML <- MLParametersEstim(x=x,pm=pm,PrintTime=TRUE)
## see the Examples folder for more examples.

StableEstim documentation built on May 30, 2017, 12:25 a.m.