These functions cooperate with each other for calculating the integral of the B-spline density basis. functions. 'distr.func.help' is the main program, calling 'poly.part', calculating the integral of the B-spline density basis in sections between neighbouring knots. 'distr.func.help' calculates analytical functions of the integral. Therefore the function 'poly.part' is needed to construct these functions.
distr.func.help(base,knots,penden.env,q,y,index)
poly.part(i,j,knots,help.env,q, yi=NULL, poly=FALSE)values of the considered B-spline basis
knots of the considered B-spline basis
Containing all information, environment of pencopula()
degree of the B-Spline basis
data of the marginal B-spline basis
columns of the whole B-spline basis, each hierarchy level is integrated separately
internal values for calculating the polynomials of each B-Spline
internal values for calculating the polynomials of each B-Spline
internal environment of pencopula() for calculating the integral
internal values for calculating the polynomials of each B-Spline
internal value, TRUE/FALSE
creating environment 'help.env', creating help points between each two neighbouring knots and calculates the integral each basis
using in 'distr.func.help' for creating the polynomial functions of each interval of each two neighbouring knots
Flexible Copula Density Estimation with Penalized Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2013), Scandinavian Journal of Statistics 40(4), 685-705.