CircNNTSRSymmetric-package {CircNNTSRSymmetric}R Documentation

CircNNTSRSymmetric: An R Package for the statistical analysis of circular data using symmetric nonnegative trigonometric sums (NNTS) models. 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)

Description

The statistical analysis of circular data using distributions based on symmetric Nonnegative Trigonometric Sums (NNTS). It includes functions to perform empirical analysis and estimate the parameters of density functions. Fernández-Durán, J.J. and Gregorio-Domínguez, M.M. (2025) <doi:10.48550/arXiv.2412.19501>.

Details

Package: CircNNTSRSymmetric
Type: Package
Version: 0.1.0
Date: 2025-02-02
License: GLP (>=2)
LazyLoad: yes

The NNTS (Non-Negative Trigonometric Sums) symmetric density around \mu is defined as:

f(\theta; M, \underline{c}, \mu)= \sum_{k=0}^M\sum_{l=0}^M \rho_k\rho_l e^{i(k-l)(\theta - \mu)}

with \rho_k real numbers for k=0, \ldots, M with \sum_{k=0}^M \rho_k^2 = \frac{1}{2\pi}.

Equivalently, the symmetric NNTS density is:

f(\theta; M, \underline{c}, \mu)= \frac{1}{2\pi}\sum_{k=0}^M\sum_{l=0}^M ||c_k|| ||\bar{c}_l|| e^{i(k-l)(\theta - \mu)} = \frac{1}{2\pi}\sum_{k=0}^M\sum_{l=0}^M c_{Sk} \bar{c}_{Sl} e^{i(k-l)\theta}

. The parameters c_{Sk}=||c_k||e^{-ik\mu} are the parameters of the general (non-symmetric) NNTS model.

The symmetric NNTS model is derived from the general NNTS model (Fernández-Durán, 2004 and Fernández-Durán and Gregorio-Domínguez, 2016) with norms (moduli) of the c parameters equal in both models and arguments of the c parameters equal to \phi_k=-k\mu for k=1,2, \ldots, M.

Author(s)

Juan Jose Fernandez-Duran and Maria Mercedes Gregorio-Dominguez

Maintainer: Maria Mercedes Gregorio Dominguez <mercedes@itam.mx>

References

Fernández-Durán, J.J. (2004). Circular Distributions Based on Nonnegative Trigonometric Sums. Biometrics, 60, pp. 499-503.

Fernández-Durán, J.J. and Gregorio-Domínguez, M.M. (2016). CircNNTSR: An R Package for the Statistical Analysis of Circular, Multivariate Circular, and Spherical Data Using Nonnegative Trigonometric Sums. Journal of Statistical Software, 70(6), 1-19. doi:10.18637/jss.v070.i06

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)


[Package CircNNTSRSymmetric version 0.1.0 Index]