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

qqgl {gld} | R Documentation

## 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/

### 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=".")

[Package gld version 2.6.2 Index]