# Arcsine-class: Class "Arcsine" In distr: Object Oriented Implementation of Distributions

## Description

The Arcsine distribution has density

1/sqrt(1+x^2)/pi

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 [email protected]

`AbscontDistribution-class` `Reals-class`
 ```1 2 3 4 5 6 7``` ```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 ```