argus (version 0.1.1)

argus-package: Generator and density for the Argus distribution

Description

Random variate generation, density, CDF and quantile function for the Argus distribution. Especially, it includes for random variate generation a flexible inversion method that is also fast in the varying parameter case. A Ratio-of-Uniforms method is provided as second alternative.

Author

Wolfgang Hörmann & Christoph Baumgarten

Details

The Argus distribution has the density (pdf) which is proportional to $$f(x) = x \sqrt{1-x^2}\exp(-0.5\chi^2(1-x^2)), \mbox{for} 0 \leq x \leq 1 \mbox{and} \chi > 0$$

Package:	argus
License:	GPL 2 or later

Package argus provides the routines:

rargus

generates argus distributed random variates.

dargus

computes the density of the argus distribution.

pargus

computes the CDF of the argus distribution.

qargus

computes the quantile function (ie. the inverse CDF )of the argus distribution.

References

Christoph Baumgarten: Random Variate Generation by Fast Numerical Inversion in the Varying Parameter Case.

Examples

## Evaluate the pdf (density)
dargus(c(0.1,0.5,0.9), chi=0.3)
## Evaluate the CDF for different chi values
pargus(c(0.1,0.5,0.9), chi=c(0.3,1.3,2.3)) 
## Evaluate the quantile function
pargus(c(0.1,0.5,0.9), chi=4.5)
## Draw a random sample
rargus(n=10, chi=0.3)
## compare histogram and density
system.time(y<-rargus(1.e5,chi=2.5))
hist(y,breaks=100,freq=FALSE)
lines(x<-seq(0,1,1.e-3),dargus(x,2.5),col=2,lwd=2)