shotGroups (version 0.7.1)

getRayParam: Estimate Rayleigh parameters sigma, mean and standard deviation

Description

Estimates the radial precision parameter sigma of the Rayleigh distribution together with the radial mean MR and radial standard deviation RSD, including parametric confidence intervals. For 1D data, it estimates the parameters of the half normal distribution. For 3D data, it estimates the parameters of the Maxwell-Boltzmann distribution

Usage

getRayParam(xy, level = 0.95, mu, doRob = FALSE)
"getRayParam"(xy, level = 0.95, mu, doRob = FALSE)
"getRayParam"(xy, level = 0.95, mu, doRob = FALSE)

Arguments

xy

either a numerical matrix with the coordinates of n points (1 row of coordinates per point), or a data frame with either the variables X, Y or Point.X, Point.Y.

level

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

mu

numerical 2-vector with the true group 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.

RSD

A vector with the RSD estimate and confidence interval bounds as named elements RSD, RSDciLo, RSDciUp.

MR

A vector with the MR estimate and confidence interval bounds as named elements MR, MRciLo, MRciUp.

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 correction factor for taking the square root. When mu is missing, the sum of squared radii is Bessel-corrected for estimating the center.

The robust estimate for the covariance matrix of (x,y)-coordinates is from covMcd using the MCD algorithm.

References

http://ballistipedia.com/index.php?title=Closed_Form_Precision

Singh, H. P. 1992. Estimation of Circular Probable Error. The Indian Journal of Statistics, Series B 5(3), 289-305.

See Also

Rayleigh, Maxwell, getCEP, getHitProb, groupSpread, covMcd

Examples

# coordinates given by a suitable data frame
getRayParam(DFtalon, level=0.95, doRob=FALSE)

# coordinates given by a matrix
## Not run: 
# xy <- matrix(round(rnorm(100, 0, 5), 2), ncol=2)
# getRayParam(xy, level=0.95, doRob=FALSE)
# ## End(Not run)