Maxwell | R Documentation |
Density, distribution function, quantile function, and random deviate generation for the Maxwell-Boltzmann distribution. The radius around the true mean in a trivariate uncorrelated normal random variable with equal variances, re-written in polar coordinates (radius, azimuth, elevation), follows a Maxwell-Boltzmann distribution.
dMaxwell(x, sigma)
pMaxwell(q, sigma, lower.tail = TRUE)
qMaxwell(p, sigma, lower.tail = TRUE)
rMaxwell(n, sigma)
x , q |
vector of quantiles. |
p |
vector of probabilities. |
n |
number of observations. If |
sigma |
vector of parameter sigma (common standard deviation of the underlying normal distribution of each 3D-coordinate). |
lower.tail |
logical. If |
The parameter sigma
may be determined with getRayParam
.
See Rayleigh
for the distribution of radial error around the true center of uncorrelated bivariate normal variables with equal variances. See Hoyt
for the distribution of radial error around the true center of correlated bivariate normal variables with unequal variances. See Rice
for the distribution of radial error around an offset center for uncorrelated bivariate normal variables with equal variances. See mvnEll
for the distribution of radial error around an offset center for correlated normal variables with unequal variances.
dMaxwell
gives the density, pMaxwell
gives the cumulative distribution function, qMaxwell
gives the quantile function, rMaxwell
generates random deviates.
The length of the result is determined by n
for rMaxwell
, and is the maximum of the lengths of the numerical parameters for the other functions.
In dMaxwell
, pMaxwell
and qMaxwell
are recycled to the length of the result. Only the first element of the logical parameters is used. In rRayleigh
, only the first element of sigma
is used.
https://reference.wolfram.com/language/ref/MaxwellDistribution.html
getRayParam
,
Rayleigh
,
Hoyt
,
Rice
,
mvnEll
dMaxwell(1, sigma=10)
pMaxwell(c(0.1, 0.5, 0.9), sigma=10)
qMaxwell(0.5, sigma=c(5, 10, 15))
rMaxwell(5, sigma=10)
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