axialnntsmanifoldnewtonestimationgradientstopsymmetric {CircNNTSRaxial} | R Documentation |
Parameter estimation for axial symmetric NNTS distributions with gradient stop
Description
Computes the maximum likelihood estimates of the parameters of an axial symmetric NNTS distribution, 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
axialnntsmanifoldnewtonestimationgradientstopsymmetric(data, M = 0, iter = 1000,
gradientstop = 1e-10, pevalmu = 1000, initialpoint = FALSE, cinitial)
Arguments
data |
Vector of axial angles in radians |
M |
Number of components in the NNTS axial model |
iter |
Number of iterations |
gradientstop |
The minimum value of the norm of the gradient to stop the Newton algorithm on the hypersphere |
pevalmu |
Number of equidistant points in the interval 0 to pi to search for the maxima of the angle of symmetry |
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. |
Value
A list with 13 elements:
cestimatessym |
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 |
mu |
Estimate of the angle of symmetry of the NNTS symmetric axial model |
logliksym |
Optimum log-likelihood value for the NNTS symmetric axial model |
AICsym |
Value of Akaike's Information Criterion for the NNTS symmetric axial model |
BICsym |
Value of Bayesian Information Criterion for the NNTS symmetric axial model |
gradnormerrorsym |
Gradient error after the last iteration for the estimation of the parameters of the NNTS symmetric axial model |
cestimatesnonsym |
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 |
logliknonsym |
Optimum log-likelihood value for the general (non-symmetric) NNTS axial model |
AICnonsym |
Value of Akaike's Information Criterion for the general (non-symmetric) NNTS axial model |
BICnonsym |
Value of Bayesian Information Criterion for the general (non-symmetric) NNTS axial model |
gradnormerrornonsym |
Gradient error after the last iteration for the estimation of the parameters of the general (non-symmetric) NNTS axial model |
loglikratioforsym |
Value of the likelihood ratio test statistic for symmetry |
loglikratioforsympvalue |
Value of the asymptotic chi squared p-value of the likelihood ratio test statistic for symmetry |
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$orientations*(pi/180)
resfeldsparsymm<-axialnntsmanifoldnewtonestimationgradientstopsymmetric(data=feldsparsangles,
M = 2, iter =1000, gradientstop=1e-10,pevalmu=1000)
resfeldsparsymm
hist(feldsparsangles,breaks=seq(0,pi,pi/7),xlab="Orientations (radians)",freq=FALSE,
ylab="",main="",ylim=c(0,.8),axes=FALSE)
axialnntsplot(resfeldsparsymm$cestimatessym[,2],2,add=TRUE)
axialnntsplot(resfeldsparsymm$cestimatesnonsym[,2],2,add=TRUE,lty=2)
axis(1,at=c(0,pi/2,pi),labels=c("0",expression(pi/2),expression(pi)),las=1)
axis(2)