# Arcsine-class

From distr v2.6
by Peter Ruckdeschel

##### Class "Arcsine"

The Arcsine distribution has density $$f(x)=\frac{1}{\pi \sqrt{1-x^2)}% }$$ for $-1

- Keywords
- distribution

##### Objects from the Class

Objects can be created by calls of the form `Arcsine()`

.
This object is an Arcsine distribution.

##### Slots

`img`

- Object of class
`"Reals"`

: The space of the image of this distribution has got dimension 1 and the name "Real Space". `r`

- Object of class
`"function"`

: generates random numbers (calls function rArcsine) `d`

- Object of class
`"function"`

: density function (calls function dArcsine) `p`

- Object of class
`"function"`

: cumulative function (calls function pArcsine) `q`

- Object of class
`"function"`

: inverse of the cumulative function (calls function qArcsine) `.withArith`

- logical: used internally to issue warnings as to interpretation of arithmetics
`.withSim`

- logical: used internally to issue warnings as to accuracy
`.logExact`

- logical: used internally to flag the case where there are explicit formulae for the log version of density, cdf, and quantile function
`.lowerExact`

- logical: used internally to flag the case where there are explicit formulae for the lower tail version of cdf and quantile function
`Symmetry`

- object of class
`"DistributionSymmetry"`

; used internally to avoid unnecessary calculations.

##### Extends

Class `"AbscontDistribution"`

, directly.
Class `"UnivariateDistribution"`

, by class `"AbscontDistribution"`

.
Class `"Distribution"`

, by class `"AbscontDistribution"`

.

##### Methods

- initialize
`signature(.Object = "Arcsine")`

: initialize method

##### See Also

##### Examples

```
A <- Arcsine()
# A is a Arcsine distribution with shape1 = 1 and shape2 = 1.
r(A)(3) # three random number generated from this distribution, e.g. 0.6979795
d(A)(c(-2,-1,-0.2,0,0.2,1,2)) # Density at x=c(-1,-0.2,0,0.2,1).
p(A)(c(-2,-1,-0.2,0,0.2,1,2)) # cdf at q=c(-1,-0.2,0,0.2,1).
q(A)(c(0,0.2,1,2)) # quantile function at at x=c(0,0.2,1).
```

*Documentation reproduced from package distr, version 2.6, License: LGPL-3*

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