gld (version 2.4.1)

fit.gpd: Estimate parameters of the GPD type generalised lambda distribution

Description

Estimates parameters of the GPD type generalised $lambda$ Distribution. Currently, only estimation via method of L moments is implemented.

The Method of L-Moments estimates for the GPD type are the only estimates for any generalised lambda distribution type with closed form expressions.

Usage

fit.gpd(x, method = "LM", na.rm = TRUE, record.cpu.time = FALSE, return.data = FALSE)
fit.gpd.lmom(data, na.rm = TRUE)
fit.gpd.lmom.given(lmoms, n = NULL)

Arguments

x

Data to be fitted, as a vector

method

A character string, to select the estimation method. Only Method of L-Moments "LM" is implemented.

na.rm

Logical: Should missing values be removed?

record.cpu.time

Logical: should the CPU time used in fitting be recorded in the fitted model object?

return.data

Logical: Should the function return the data (from the argument x)?

data

Data to be fitted, as a vector

lmoms

A numeric vector containing two L-moments and two L-moment ratios, in the order $l_1, l_2, t_3, t_4$.

n

the sample size, defaults to NULL

Value

These funciton return an object of class "GldFitMultiple". It is a list, containing these components (optional components noted here);Each of the estimate elements (if they are not NA) are a vector of length 4, giving the estimated parameters, in order;$alpha$ - location parameter $beta$ - scale parameter $delta$ - skewness parameter $lambda$ - kurtosis parameter

Details

The method of L-Moments equates sample L-Moments with expressions for the L-Moments of the GPD type GLD. Closed form expressions exist to give these estimates.

For many values there are two possible estimates for the same L Moment values, one in each of two regions of the GPD GLD parameter space, denoted region A and region B in van Staden (2013). More details on these regions can be found on page 154 of van Staden (2013).

If the 4th L-Moment ratio, $tau4$ is less than the minimum value that $tau4$ can obtain for the GPD generalised lambda distribution;

$$\tau_4^{(min)}=\frac{12-5\sqrt{6}}{12+5\sqrt{6}} \approx -0.0102051,$$

there is no possible estimate (from either region A or B), and this function returns NA for the estimates.

References

Van Staden, Paul J., & M.T. Loots. (2009), Method of L-moment Estimation for the Generalized Lambda Distribution. In Proceedings of the Third Annual ASEARC Conference. Callaghan, NSW 2308 Australia: School of Mathematical and Physical Sciences, University of Newcastle.

See Also

GeneralisedLambdaDistribution

Examples

fit.gpd.lmom.given(c(1,.3,.6,.8))