IntKde {asymmetry.measures} R Documentation

## Integrated Kernel density estimator

### Description

Classical univariate integrated kernel density estimator

### Usage

  IntKde(xin, xout, h, kfun)


### Arguments

 xin A vector of data points - the available sample size. xout grid points where the distribution function will be estimated. h The bandwidth parameter. Defaults to 3.572*σ*n^{-1/3} according to Bowman et al.(1998). kfun The kernel to use in the distribution function estimate.

### Details

It implements the classical density integrated kernel estimator.

Let X_1,X_2,…, X_n be a univariate independent and identically distributed sample drawn from some unknown distribution function F. Its kernel density estimator is

\hat{F}(x)= n^{-1}∑_{i=1}^n K≤ft \{ (x-X_i)h^{-1}\right \}

where K is an integrated kernel, and h > 0 is a smoothing parameter called the bandwidth.

### Value

Returns a vector with the estimate of the distribution function at the user specified grid points.

### Author(s)

Dimitrios Bagkavos and Lucia Gamez Gallardo

R implementation and documentation: Dimitrios Bagkavos <dimitrios.bagkavos@gmail.com>, Lucia Gamez Gallardo <gamezgallardolucia@gmail.com>

### See Also

bw.nrd, bw.nrd0, bw.ucv, bw.bcv

### Examples

x.in <- rnorm(100)
x.out <- seq(-3.4,3.4,length=60)
kernel <- IntEpanechnikov
dist.est <- IntKde(xin=x.in,xout=x.out,kfun=kernel)
plot(x.out,dist.est, type="l", col="red", main="Kernel c.d.f. estimator")


[Package asymmetry.measures version 0.2 Index]