CircNNTSR (version 2.3)

nntsuniformitytestlikelihoodratio: Computes the statistic and critical values of the circular uniformity test

Description

Computes the statistic and critical values at 10%, 5% and 1% of the circular uniformity test based on the NNTS likelihood ratio for M values from 1 to 7 and any sample size.

Usage

nntsuniformitytestlikelihoodratio(data,M=1, iter=1000, initialpoint = FALSE,
cinitial,gradientstop=1e-10)

Value

gradient

Gradient error after the last iteration

likratiounifstat

Value of the likelihood ratio NNTS circular uniformity test statistic

criticalvalue10percent

Critical value at a 10% significance level of the likelihood ratio NNTS circular uniformity test

criticalvalue05percent

Critical value at a 5% significance level of the likelihood ratio NNTS circular uniformity test

criticalvalue01percent

Critical value at a 1% significance level of the likelihood ratio NNTS circular uniformity test

Arguments

data

Vector of angles in radians

M

Number of components in the NNTS

iter

Number of iterations

initialpoint

TRUE if an initial point for the optimization algorithm 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 \(c_1, \ldots ,c_M\)). The sum of the squared moduli of the parameters must be equal to \(\frac{1}{2\pi}\)

.

gradientstop

The value of the gradient of the Newton algorithm at which the algorithms stops

Author

Juan Jose Fernandez-Duran and Maria Mercedes Gregorio-Dominguez

References

Fernandez-Duran and J. J. and Gregorio-Dominguez and M. M (2022). Sums of Independent Circular Random Variables and Maximum Likelihood Circular Uniformity Tests Based on Nonnegative Trigonometric Sums Distributions, arXiv preprint arXiv:2212.01416

Examples

set.seed(200)
a<-2*pi*runif(50)
#NNTS likelihood ratio circular uniformity test for M=2 and gradientstop at 1e-09
nntsuniformitytestlikelihoodratio(data=a,M=2,gradientstop=1e-09)
data(Turtles_radians)
#NNTS likelihood ratio circular uniformity test for M=5 and gradientstop at 1e-12
nntsuniformitytestlikelihoodratio(data=Turtles_radians,M=5,gradientstop=1e-09)