skewunit (version 1.0)

asin: The ArcSin distribution.

Description

Density, distribution function and random generation for the ArcSin distribution.

Usage

dasin(x, log=FALSE)
pasin(q, lower.tail=TRUE, log.p=FALSE)
rasin(n)

Value

dasin gives the density, pasin gives the distribution function, and rasin generates random deviates. The length of the result is determined by n for rasin, and is the maximum of the lengths of the numerical arguments for the other functions. The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.

Arguments

x, q

vector of quantiles.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

log, log.p

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are $P[X\le x]$, otherwise, $P[X>x]$.

Author

Diego Gallardo

Details

The ArcSin distribution has density $$f(x)=\frac{1}{\pi \sqrt{x(1-x)}},x\in (0,1),$$ and cumulative distribution function $$F(x)=\frac{2}{\pi }Arcsin(\sqrt{x}),x\in (0,1).$$

References

Arnold, B.C. and Groeneveld, R.A. (1980). Some Properties of the Arcsine Distribution. Journal of the Ammerican Statistical Association, 75, 173-175.

Examples

dasin(0.5)
pasin(0.5)
rasin(5)