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, ...)
A list of the same form as that returned by qqline
The x coordinates of the points that were/would be plotted, corresponding to a generalised lambda distibution with parameters \(\lambda_1\), \(\lambda_2\), \(\lambda_3\), \(\lambda_4\).
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
The data sample
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.
\(\lambda_2\) - scale parameter
\(\lambda_3\) - first shape parameter
\(\lambda_4\) - second shape parameter
\(\lambda_5\) - a skewing parameter, in the fm5 parameterisation
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)
A logical value, TRUE adds a line through the origian with a slope of 1 to the plot
Parameters of the generalised lambda
distribution (see lambda1
to lambda4
for details.
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
parameterisation to use for the second set of parameter values
Number of quantiles to use in a Q-Q plot comparing two sets of parameter values
graphical parameters, passed to qqplot
Robert King, robert.king.newcastle@gmail.com, https://github.com/newystats/
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.
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
gld
,starship
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=".")
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