gld: qqgl – R documentation

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qqgl

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, robert.king@newcastle.edu.au, https://tolstoy.newcastle.edu.au/~rking/

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://tolstoy.newcastle.edu.au/~rking/gld/

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

Estimation and Use of the Generalised (Tukey) Lambda Distribution

v2.6.2

GPL (>= 2)

Authors

Robert King <Robert.King@newcastle.edu.au>, Benjamin Dean <Benjamin.Dean@uon.edu.au>, Sigbert Klinke, Paul van Staden

Initial release

2020-01-07