rotations (version 1.6.3)

prentice: 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 Q4
prentice(x, alp = NULL)
# S3 method for 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.

Value

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

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

See Also

bayesCR, fisheretal, chang, zhang

Examples

# NOT RUN {
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)
# }