qqsl {sld}

Quantile-Quantile plot against the skew logistic distribution

Description

qqgl produces a Quantile-Quantile plot of data against the quantile-based skew logistic distribution, or a Q-Q plot to compare two sets of parameter values for the quantile-based skew logistic distribution. This function does for the skew logistic distribution what qqnorm does for the normal.

Usage

qqsl(y=NULL,parameters1,parameters2=NULL,abline=TRUE,
      granularity.for.2.dists=4000,use.endpoints=FALSE,...)

Arguments

y

The data sample

parameters1

A vector of length 3, containg the parameters of the skew logistic distribution, \alpha, \beta and \delta.

parameters2

Second set of parameters of the skew logistic distribution. A vector of length 3, as described above for parameters1.

abline

A logical value, TRUE adds a line through the origian with a slope of 1 to the plot

granularity.for.2.dists

Number of quantiles to use in a Q-Q plot comparing two sets of parameter values

use.endpoints

logical. When comparing two sets of parameter values, should Q(0) and Q(1) be used? TRUE will give QQ plots including the theoretical minimum and maximum of the distribution, which is arguably not equivalent to what would be seen in QQ plots based on data. FALSE will give QQ plots based on ideal depths (type 8 quantiles, see quantile documentation), where n is the granularity.for.2.dists.

...

graphical parameters, passed to qqplot

Details

See sld for more details on the Skew Logistic 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 skew logistic distibution with parameters \alpha, \beta and \delta.

y

The original y vector, i.e., the corresponding y coordinates, or a corresponding set of quantiles from a skew logistic distribution with the second set of parameters

Author(s)

Robert King, [e-mail], https://github.com/newystats/sld and Paul van Staden

References

van Staden, P.J. and King, R.A.R. (2015) The quantile-based skew logistic distribution, Statistics and Probability Letters 96 109–116. doi: 10.1016/j.spl.2014.09.001

van Staden, Paul J. 2013 Modeling of generalized families of probability distribution in the quantile statistical universe. PhD thesis, University of Pretoria. http://hdl.handle.net/2263/40265

https://github.com/newystats/sld

See Also

sld

Examples

qqsl(y=rsl(100,c(0,1,0.7)),parameters1=c(0,1,0.7))
qqsl(parameters1=c(0,1,0.7),parameters2=c(0,0.9,0.5),col="blue")