Maxwell {rotations} | R Documentation |
The modified Maxwell-Boltzmann distribution
Description
Density, distribution function and random generation for the Maxwell-Boltzmann distribution with
concentration kappa
\kappa
restricted to the range [-\pi,\pi)
.
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 |
Haar |
logical; if TRUE density is evaluated with respect to the Haar measure. |
lower.tail |
logical; if TRUE (default) probabilities are |
n |
number of observations. If |
Details
The Maxwell-Boltzmann distribution with concentration \kappa
has density
C_\mathrm{{M}}(r|\kappa)=2\kappa\sqrt{\frac{\kappa}{\pi}}r^2e^{-\kappa r^2}
with respect to Lebesgue measure. The usual expression for the Maxwell-Boltzmann distribution can be recovered by
setting a=(2\kappa)^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)