pencopula (version 0.2.1)

distr.func.help: These functions are used for calculating the integral of the B-spline density basis.

Description

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.

Usage

distr.func.help(base,knots,penden.env,q,y,index)
poly.part(i,j,knots,help.env,q, yi=NULL, poly=FALSE)

Arguments

base

values of the considered B-spline basis

knots

knots of the considered B-spline basis

penden.env

Containing all information, environment of pencopula()

q

degree of the B-Spline basis

y

data of the marginal B-spline basis

index

columns of the whole B-spline basis, each hierarchy level is integrated separately

i

internal values for calculating the polynomials of each B-Spline

j

internal values for calculating the polynomials of each B-Spline

help.env

internal environment of pencopula() for calculating the integral

yi

internal values for calculating the polynomials of each B-Spline

poly

internal value, TRUE/FALSE

Value

• distr.func.help
  creating environment 'help.env', creating help points between each two neighbouring knots and calculates the integral each basis
• poly.part
  using in 'distr.func.help' for creating the polynomial functions of each interval of each two neighbouring knots

References

Flexible Copula Density Estimation with Penalized Hierarchical B-Splines, Kauermann G., Schellhase C. and Ruppert, D. (2011), to appear.