getHoytParam {shotGroups} | R Documentation |
Determine parameters q and omega of the Hoyt distribution
Description
Determines the Hoyt distribution's shape parameter q and scale parameter omega from the eigenvalues of a (2 x 2)-covariance matrix.
Usage
getHoytParam(x)
## S3 method for class 'matrix'
getHoytParam(x)
## S3 method for class 'list'
getHoytParam(x)
## S3 method for class 'data.frame'
getHoytParam(x)
## Default S3 method:
getHoytParam(x)
Arguments
x |
one of the following: a (2 x 2)-covariance matrix, a list of (2 x 2)-covariance matrices, a data frame with either the variables |
Details
The parameters q
and omega
derive from the eigenvalues ev1, ev2 of the covariance matrix of the bivariate normal distribution as follows: q = 1 / sqrt(((ev1+ev2)/ev2) - 1)
and omega = ev1 + ev2
.
If x
is a data frame, its sample covariance matrix is used to estimate the eigenvalues. Note that the Hoyt distribution is only approximately valid for large samples if estimated parameters are used.
Value
A list with the following components:
q |
A vector with values of the shape parameter |
omega |
A vector with values of the scale parameter |
References
Hoyt, R. S. (1947). Probability functions for the modulus and angle of the normal complex variate. Bell System Technical Journal, 26(2), 318-359.
https://reference.wolfram.com/language/ref/HoytDistribution.html
See Also
Examples
## q and omega based on coordinates in a data frame
getHoytParam(DFscar17)
## q and omega based on a covariance matrix
cm1 <- cbind(c(8, 0), c(0, 2))
getHoytParam(cm1)
## q and omega based on a list of covariance matrices
cm2 <- cbind(c(6, 0), c(0, 4))
cmL <- list(cm1, cm2)
getHoytParam(cmL)
## q and omega based on eigenvalues
ev <- eigen(cm1)$values
getHoytParam(cm1)