Arcsine-class {distr} | R Documentation |

## Class "Arcsine"

### Description

The Arcsine distribution has density

```
f(x)=\frac{1}{\pi \sqrt{1-x^2}%
}
```

for `-1 < x < 1`

.

### 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

### Author(s)

Peter Ruckdeschel peter.ruckdeschel@uni-oldenburg.de

### See Also

`AbscontDistribution-class`

`Reals-class`

### 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).
## in RStudio or Jupyter IRKernel, use q.l(A)(c(0,0.2,1,2)) instead
```

*distr*version 2.9.3 Index]