Maxwell: The modified Maxwell-Boltzmann distribution

In rotations: Working with Rotation Data

The modified Maxwell-Boltzmann distribution

Description

Density, distribution function and random generation for the Maxwell-Boltzmann distribution with concentration kappa κ restricted to the range [-π,π).

Usage

dmaxwell(r, kappa = 1, nu = NULL, Haar = TRUE)

pmaxwell(q, kappa = 1, nu = NULL, lower.tail = TRUE)

rmaxwell(n, kappa = 1, nu = NULL)

Arguments

r, q	vector of quantiles.
kappa	concentration parameter.
nu	circular variance, can be used in place of kappa.
Haar	logical; if TRUE density is evaluated with respect to the Haar measure.
lower.tail	logical; if TRUE (default) probabilities are P(X≤ x) otherwise, P(X>x).
n	number of observations. If length(n)>1, the length is taken to be the number required.

Details

The Maxwell-Boltzmann distribution with concentration κ has density

C(r|κ)=2κ(κ/π)^(1/2)r^2exp(-κ r^2)

with respect to Lebesgue measure. The usual expression for the Maxwell-Boltzmann distribution can be recovered by setting a=(2κ)^0.5.

bingham2010

Value

dmaxwell	gives the density
pmaxwell	gives the distribution function
rmaxwell	generates a vector of random deviates

See Also

Angular-distributions for other distributions in the rotations package.

Examples

r <- seq(-pi, pi, length = 500)

#Visualize the Maxwell-Boltzmann density fucntion with respect to the Haar measure
plot(r, dmaxwell(r, kappa = 10), type = "l", ylab = "f(r)")

#Visualize the Maxwell-Boltzmann density fucntion with respect to the Lebesgue measure
plot(r, dmaxwell(r, kappa = 10, Haar = FALSE), type = "l", ylab = "f(r)")

#Plot the Maxwell-Boltzmann CDF
plot(r,pmaxwell(r,kappa = 10), type = "l", ylab = "F(r)")

#Generate random observations from Maxwell-Boltzmann distribution
rs <- rmaxwell(20, kappa = 1)
hist(rs, breaks = 10)

rotations documentation built on June 25, 2022, 1:06 a.m.