axialnntsmanifoldnewtonestimationgradientstopknownmusymmetric {CircNNTSRaxial} | R Documentation |
Parameter estimation for axial symmetric NNTS distributions with known location angle gradient stop
Description
Computes the maximum likelihood estimates of the parameters of an axial symmetric NNTS distribution with known location angle, using a Newton algorithm on the hypersphere and considering a maximum number of iterations determined by a constraint in terms of the norm of the gradient
Usage
axialnntsmanifoldnewtonestimationgradientstopknownmusymmetric(data, muknown=0, M = 0,
iter = 1000, initialpoint = FALSE, cinitial,gradientstop=1e-10)
Arguments
data |
Vector of axial angles in radians |
muknown |
Value of the known location angle |
M |
Number of components in the NNTS axial model |
iter |
Number of iterations |
initialpoint |
TRUE if an initial point for the optimization algorithm for the axial NNTS density will be used |
cinitial |
Vector of size M+1. The first element is real and the next M elements are complex (values for $c_0$ and $c_1, ...,c_M$). The sum of the squared moduli of the parameters must be equal to 1/pi. This is the vector of parameters for the general (asymmetric) NNTS axial density |
gradientstop |
The minimum value of the norm of the gradient to stop the Newton algorithm on the hypersphere |
Value
A list with 13 elements:
cestimatesmuknown |
Matrix of (M+1)x2. The first column is the parameter numbers, and the second column is the c parameter's estimators of the symmetric NNTS axial model with known location angle |
muknown |
Known value of the location angle of the symmetric NNTS axial model |
loglikmuknown |
Optimum log-likelihood value for the symmetric NNTS axial model with known location angle |
AICmuknown |
Value of Akaike's Information Criterion for the symmetric NNTS axial model with known location angle |
BICmuknown |
Value of Bayesian Information Criterion for the symmetric NNTS axial model with known location angle |
gradnormerrormuknown |
Gradient error after the last iteration for the estimation of the parameters of the symmetric NNTS axial model with known location angle |
cestimatesmuunknown |
Matrix of (M+1)x2. The first column is the parameter numbers, and the second column is the c parameter's estimators of the general (non-symmetric) NNTS axial model with unknown location angle |
loglikmuunknown |
Optimum log-likelihood value for the general (non-symmetric) NNTS axial model with unknown location angle |
AICmuunknown |
Value of Akaike's Information Criterion for the general (non-symmetric) NNTS axial model with unknown location angle |
BICmuunknown |
Value of Bayesian Information Criterion for the general (non-symmetric) NNTS axial model with unknown location angle |
gradnormerrormuunknown |
Gradient error after the last iteration for the estimation of the parameters of the general (non-symmetric) NNTS axial model with unknown location angle |
loglikratioformuknown |
Value of the likelihood ratio test statistic for known location angle |
loglikratioformuknownpvalue |
Value of the asymptotic chi squared p-value of the likelihood ratio test statistic for known location angle |
Author(s)
Juan Jose Fernandez-Duran and Maria Mercedes Gregorio-Dominguez
References
Fernandez-Duran, J.J. and Gregorio-Dominguez, M.M. (2025). Multimodal distributions for circular axial data. arXiv:2504.04681 [stat.ME] (available at https://arxiv.org/abs/2504.04681)
Fernández-Durán, J.J., Gregorio-Domínguez, M.M. (2025). Multimodal Symmetric Circular Distributions Based on Nonnegative Trigonometric Sums and a Likelihood Ratio Test for Reflective Symmetry, arXiv:2412.19501 [stat.ME] (available at https://arxiv.org/abs/2412.19501)
Examples
data(Datab2fisher)
feldsparsangles<-Datab2fisher
feldsparsangles<-feldsparsangles$orientations*(pi/180)
resfeldsparknownanglesymmetric<-axialnntsmanifoldnewtonestimationgradientstopknownmusymmetric(
data=feldsparsangles, muknown=pi/3, M = 3, iter =1000, gradientstop=1e-10)
resfeldsparknownanglesymmetric
hist(feldsparsangles,breaks=seq(0,pi,pi/7),xlab="Orientations (radians)",freq=FALSE,
ylab="",main="",ylim=c(0,.8),axes=FALSE)
axialnntsplot(resfeldsparknownanglesymmetric$cestimatesmuunknown[,2],3,add=TRUE)
axialnntsplot(resfeldsparknownanglesymmetric$cestimatesmuknown[,2],3,add=TRUE,lty=2)
axis(1,at=c(0,pi/2,pi),labels=c("0",expression(pi/2),expression(pi)),las=1)
axis(2)