Arcsine-class {distr}

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 [e-mail]

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