prentice {rotations}

Transformation based asymptotic confidence region

Description

Find the radius of a 100(1-\alpha)% confidence region for the projected mean based on a result from directional statistics.

Usage

prentice(x, alp)

## S3 method for class 'Q4'
prentice(x, alp = NULL)

## S3 method for class 'SO3'
prentice(x, alp = NULL)

Arguments

x

n\times p matrix where each row corresponds to a random rotation in matrix (p=9) or quaternion (p=4) form.

alp

alpha level desired, e.g. 0.05 or 0.10.

Details

Compute the radius of a 100(1-\alpha)% confidence region for the central orientation based on the projected mean estimator using the method due to prentice1986. For a rotation specific version see rancourt2000. The variability in each axis is different so each axis will have its own radius.

prentice1986, rancourt2000

Value

Radius of the confidence region centered at the projected mean for each of the x-, y- and z-axes.

See Also

bayesCR, fisheretal, chang, zhang

Examples

Qs<-ruars(20, rcayley, kappa = 100, space = 'Q4')

# The prentice method can be accessed from the "region" function or the "prentice" function
region(Qs, method = "transformation", type = "asymptotic", alp = 0.1, estimator = "mean")
prentice(Qs, alp = 0.1)