# distr.func.help: These functions are used for calculating the integral of the... In pencopula: Flexible Copula Density Estimation with Penalized Hierarchical B-Splines

## 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

 ```1 2``` ```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

## Author(s)

Christian Schellhase <cschellhase@wiwi.uni-bielefeld.de>

## References

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.

pencopula documentation built on May 2, 2019, 7:21 a.m.