rotations (version 0.1)

Haar: Uniform distribution on $SO(3)$

Description

Density, distribution function and random generation for the uniform distribution on $SO(3)$.

Usage

dhaar(r)
  phaar(q, lower.tail = TRUE)
  rhaar(n)

Arguments

r,q

vector of quantiles.

n

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

lower.tail

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

Value

• dhaar
  gives the density
• phaar
  gives the distribution function
• rhaar
  generates random deviates

Details

The uniform distribution on the space $SO(3)$ (also referred to as the Haar measure) has density $$C_U(r)=\frac{[1-cos(r)]}{2\pi}.$$

See Also

Angular-distributions for other distributions in the rotations package.