Quantile-Quantile plot against the generalised lambda distribution

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.

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

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=".")