mnntsloglik {CircNNTSR}

MNNTS log-likelihood function

Description

Computes the log-likelihood function with MNNTS density for data

Usage

mnntsloglik(data, cpars = 1/sqrt(2 * pi), M = 0, R = 1)

Arguments

data

Matrix of angles in radians, a column for each dimension, a row for each data point.

cpars

Parameters of the model. A vector of complex numbers of dimension prod(M+1). The first element is a real and positive number. The first M[1]+1 elements correspond to dimension one, next M[2]+1 elements correspond to dimension two, and so on. The sum of the SQUARED moduli of the c parameters must be equal to \left(\frac{1}{2*pi}\right)^R.

M

Vector of length R with number of components in the MNNTS for each dimension.

R

Number of dimensions.

Value

The function returns the value of the log-likelihood function for the data.

Author(s)

Juan Jose Fernandez-Duran and Maria Mercedes Gregorio-Dominguez

References

Fernandez-Duran, J.J. and Gregorio-Dominguez, M.M. (2009) Multivariate Angular Distributions Based on Multiple Nonnegative Trigonometric Sums, Working Paper, Statistics Department, ITAM, DE-C09.1

Examples

M<-c(2,3)
R<-length(M)
data<-c(0,pi,pi/2,pi,pi,3*pi/2,pi,2*pi,2*pi,pi)
data<-matrix(data,ncol=2,byrow=TRUE)
data
ccoef<-mnntsrandominitial(M,R)
mnntsdensity(data,ccoef,M,R)
mnntsloglik(data,ccoef,M,R)