shotGroups (version 0.8.2)

getRiceParam: Estimate Rice parameters nu and sigma

Description

Estimates the location parameter nu and the scale parameter sigma of the Rice distribution together with the radial mean MR and radial standard deviation RSD based on a set of 2D-coordinates. Includes the parametric confidence interval for sigma.

Usage

getRiceParam(xy, level = 0.95, doRob = FALSE, type = c('LiZhangDai', 'MOM'))
# S3 method for data.frame
getRiceParam(xy, level = 0.95, doRob = FALSE, type=c('LiZhangDai', 'MOM'))
# S3 method for default
getRiceParam(xy, level = 0.95, doRob = FALSE, type=c("LiZhangDai", 'MOM'))

Value

A list with the estimates for nu, sigma, RSD, and MR including the confidence interval for sigma.

nu

The estimated location parameter nu.

sigma

A vector with the sigma estimate and confidence interval bounds as named elements sigma, sigCIlo, sigCIup.

MR

The MR estimate.

RSD

The RSD estimate.

Arguments

xy

either a numerical (n x 2)-matrix with the (x,y)-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 interval for sigma.

doRob

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

type

The initial biased nu estimate is the Euclidean norm of the group center. For 'LiZhangDai', the bias-correction from Liu et al., 2009. For 'MOM', the estimated bias is subtracted. If the estimated bias is larger than the initial estimate, the final estimate is then set to 0.

Details

The sigma estimate uses getRayParam. The robust estimate for the center and for the covariance matrix of (x,y,z)-coordinates is from covMcd using the MCD algorithm.

References

https://reference.wolfram.com/language/ref/RiceDistribution.html

Li, Q., Zhang, J., & Dai, S. (2009). On estimating the non-centrality parameter of a chi-squared distribution. Statistics and Probability Letters 79, 98-114.

See Also

Rice, getRayParam, getCEP, getHitProb, covMcd

Examples

getRiceParam(DF300BLKhl, level=0.95, doRob=FALSE)

# coordinates given by a matrix
if (FALSE) {
xy <- matrix(round(rnorm(60, 0, 5), 2), ncol=2)
getRiceParam(xy, level=0.95, doRob=FALSE)
}