distr.func: These functions are used for calculating the empirical and theoretical distribution functions.

Description

These functions cooperate with each other for calculating the distribution functions. 'distr.func' is the main program, calling 'distr.func.help',generating an environment with needed values for calculating the distribution of each interval between two neighbouring knots. 'distr.func' returns analytical functions of the distribution of each interval between two neighbouring knots. Therefore the function 'poly.part' is needed to construct these functions. 'cal.int' evaluates these integrals, considering if the whole interval should be evaluated or if any discrete value 'yi' is of interest.

Usage

distr.func(yi = NULL, obj, help.env=distr.func.help(obj))
distr.func.help(obj)
cal.int(len.b, q, help.env, knots.val)
poly.part(i,j,knots.val,help.env,q, yi=NULL, poly=FALSE)

Arguments

if the distribution at any discrete point is of interest, you can call for it. Default=NULL doesn't consider any discrete point

obj

a object of class pendensity

help.env

object is generated with calling distr.func.help(obj)

len.b

length of B-Spline

order of the B-Spline

knots.val

values of the used knots

poly

TRUE/FALSE

internal values for calculating the polynomials of each B-Spline

Value

distr.funcreturns analytical functions of the distributions between each two neighbouring intervals
distr.func.helpcreating environment 'help.env', creating help points between each two neighbouring knots and calculates the polynomial-coefficients of each base part
cal.intevaluating the result of distr.func. Thereby it's possible to call for an explicit distribution values F(yi)
poly.partusing in 'distr.func' for creating the polynomial functions of each interval of each two neighbouring knots

References

Density Estimation with a Penalized Mixture Approach, Schellhase C. and Kauermann G. (2012), Computational Statistics 27 (4), p. 757-777.