# plotsl: Plots of density and distribution function for the quantile... In sld: Estimation and Use of the Quantile-Based Skew Logistic Distribution

## Description

Produces plots of density and distribution function for the quantile based skew logistic distribution. Although you could use `curve(dsl(x))` to do this, the fact that the density and quantiles of this distribution are defined in terms of the depth, u, means that a seperate function that uses the depths to produce the values to plot is more accurate and efficient.

## Usage

 ```1 2 3 4``` ```plotsld(parameters, add=FALSE, granularity = 10000, xlab = "x", ylab="density", quant.probs = seq(0,1,.25), ...) plotslc(parameters, add=FALSE, granularity = 10000, xlab = "quantile", ylab="depth", quant.probs = seq(0,1,.25), ...) ```

## Arguments

 `parameters` A vector of length 3, giving the parameters of the quantile-based skew logistic distribution. The 3 elements are alpha (location), beta (scale) and delta (skewing). alpha can take on any real value, beta can take on any positive value and delta must satisfy 0 <= delta <= 1. delta = 0.5 gives the logistic distribution, delta = 0 gives the reflected exponential distribution and delta = 1 gives the exponential distribution. `add` Should this add to an existing plot (using `lines`) or produce a new plot (using `plot`). `granularity` Number of points at which quantiles and density will be calculated.— see details `xlab` X axis label `ylab` Y axis label `quant.probs` Quantiles of distribution to return (see value below). Set to NULL to suppress this return entirely. `...` arguments that get passed to `plot` if this is a new plot

## Details

The quantile-based skew logistic distribution is defined by its quantile function. The density of the distribution is available explicitly as a function of depths, u, but not explicitly available as a function of x (except for the special cases at delta=0,0.5 and 1). This function calculates quantiles and density as a function of depths to produce a density plot `plotsld` or cumulative probability plot `plotslc`.

## Value

A number of quantiles from the distribution, the default being the minimum, maximum and quartiles.

## References

van Staden, P.J. and King, Robert A.R. (2015) The quantile-based skew logistic distribution, Statistics and Probability Letters 96, 109–116. http://dx.doi.org/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

`sld`
 ```1 2 3 4``` ```plotsld(c(0,1,1),main="Exponential Distribution") plotsld(c(0,1,0.5),main="Logistic Distribution") plotsld(c(0,1,0.7)) plotslc(c(0,1,0.7)) ```