qqgl: Quantile-Quantile plot against the generalised lambda...

In gld: Estimation and Use of the Generalised (Tukey) Lambda Distribution

Quantile-Quantile plot against the generalised lambda distribution

Description

qqgl produces a Quantile-Quantile plot of data against the generalised lambda distribution, or a Q-Q plot to compare two sets of parameter values for the generalised lambda distribution. It does for the generalised lambda distribution what qqnorm does for the normal.

Usage

qqgl(y = NULL, lambda1 = 0, lambda2 = NULL, lambda3 = NULL, lambda4 = NULL, 
  param = "fkml", lambda5 = NULL, abline = TRUE, lambda.pars1 = NULL, lambda.pars2 = NULL,
  param2 = "fkml", points.for.2.param.sets = 4000, ...)

Arguments

y	The data sample
lambda1	This can be either a single numeric value or a vector. If it is a vector, it must be of length 4 for parameterisations fmkl or rs and of length 5 for parameterisation fm5. If it is a vector, it gives all the parameters of the generalised lambda distribution (see below for details) and the other lambda arguments must be left as NULL. Alternatively, leave lambda1 as the default value of 0 and use the lambda.pars1 argument instead. If it is a a single value, it is lambda 1, the location parameter of the distribution and the other parameters are given by the following arguments Note that the numbering of the lambda parameters for the fmkl parameterisation is different to that used by Freimer, Mudholkar, Kollia and Lin.
lambda2	lambda 2 - scale parameter
lambda3	lambda 3 - first shape parameter
lambda4	lambda 4 - second shape parameter
lambda5	lambda 5 - a skewing parameter, in the fm5 parameterisation
param	choose parameterisation: fmkl uses Freimer, Mudholkar, Kollia and Lin (1988) (default). rs uses Ramberg and Schmeiser (1974) fm5 uses the 5 parameter version of the FMKL parameterisation (paper to appear)
abline	A logical value, TRUE adds a line through the origian with a slope of 1 to the plot
lambda.pars1	Parameters of the generalised lambda distribution (see lambda1 to lambda4 for details.
lambda.pars2	Second set of parameters of the generalised lambda distribution (see lambda1 to lambda4 for details. Use lambda.pars1 and lambda.pars2 to produce a QQ plot comparing two generalised lambda distributions
param2	parameterisation to use for the second set of parameter values
points.for.2.param.sets	Number of quantiles to use in a Q-Q plot comparing two sets of parameter values
...	graphical parameters, passed to qqplot

Details

See gld for more details on the Generalised Lambda Distribution. A Q-Q plot provides a way to visually assess the correspondence between a dataset and a particular distribution, or between two distributions.

Value

A list of the same form as that returned by qqline

x	The x coordinates of the points that were/would be plotted, corresponding to a generalised lambda distibution with parameters lambda 1, lambda 2, lambda 3, lambda 4.
y	The original y vector, i.e., the corresponding y coordinates, or a corresponding set of quantiles from a generalised lambda distribution with the second set of parameters

Author(s)

Robert King, [e-mail], https://github.com/newystats/

References

King, R.A.R. & MacGillivray, H. L. (1999), A starship method for fitting the generalised lambda distributions, Australian and New Zealand Journal of Statistics 41, 353–374

https://github.com/newystats/gld/

See Also

gld,starship

Examples

qqgl(rgl(100,0,1,0,-.1),0,1,0,-.1)
qqgl(lambda1=c(0,1,0.01,0.01),lambda.pars2=c(0,.01,0.01,0.01),param2="rs",pch=".")

gld documentation built on Oct. 23, 2022, 5:05 p.m.