shotGroups (version 0.6.2)

getMaxParam: Estimate Maxwell-Boltzmann parameters sigma, mean and standard deviation

Description

Estimates the scale parameter sigma of the Maxwell-Boltzmann distribution together with the radial mean MR and radial standard deviation RSD, including parametric confidence intervals.

Usage

getMaxParam(xyz, level = 0.95, mu, doRob = FALSE)

## S3 method for class 'data.frame':
getMaxParam(xyz, level = 0.95, mu, doRob = FALSE)

## S3 method for class 'default':
getMaxParam(xyz, level = 0.95, mu, doRob = FALSE)

Arguments

xyz

either a numerical (n x 3)-matrix with the coordinates of n points (1 row of (x,y,z)-coordinates per point), or a data frame with either the variables X, Y, Z or Point.X, Point.Y, Poin

level

a numerical value with the coverage for the confidence intervals for sigma, MR, RSD.

mu

true distribution center (optional). See details.

doRob

logical: use robust estimation of covariance matrix as basis for estimators?

Value

• A list with the estimates for sigma, RSD, and MR including the confidence intervals.
• sigma
  A vector with the sigma estimate and confidence interval bounds as named elements sigma, sigCIlo, sigCIup.
• MR
  A vector with the MR estimate and confidence interval bounds as named elements MR, MRciLo, MRciUp.
• RSD
  A vector with the RSD estimate and confidence interval bounds as named elements RSD, RSDciLo, RSDciUp.

Details

When the true mean mu of the distribution is given, the sigma estimate uses the sum of squared radii for the variance estimate (the total un-corrected variance of the coordinates), and employs the c4(3*N+1) correction factor and for taking the square root. When mu is missing, the sum of squared radii is Bessel-corrected for estimating the center, and c4(3*N-2) is used. MR and RSD each are a constant fraction of sigma. The robust estimate for the covariance matrix of (x,y,z)-coordinates is from covMcd using the MCD algorithm.

References

http://reference.wolfram.com/language/ref/MaxwellDistribution.html

See Also

Maxwell, getCEP, getHitProb, covMcd

Examples

# coordinates given by a matrix
xyz <- matrix(round(rnorm(60, 0, 5), 2), ncol=3)
getMaxParam(xyz, doRob=FALSE)