# Getting a cdf equal to 1 from a variable kernel density estimation

#### Lio67

##### New Member
When I integrate the variable kernel density estimation of a sample from -inf to inf, I should get 1. But it is not what I get with my code below. I find a value higher than 2. How can I fix this?

n<-1000
df <- data.frame(x=unlist(lapply(1, function(i) rnorm(n, 0,sd=1))))
df<-as.data.frame(df[order(df$x),]) names(df)[1]<-"x" library(functional) gaussianKernel <- function(u, h) exp(-sum(u^2)/(2*h^2)) densityFunction <- function(x, df, ker, h) { difference = t(t(df) - x) W = sum(apply(difference, 1, ker, h=h)) W/(nrow(df)*(h^(length(df)))) } myDensityFunction <- Curry(densityFunction, df=df, ker=gaussianKernel , h=2) vect<-vector() for (i in 1:length(df$x)){
f<-myDensityFunction(df$x) vect<-c(vect,f) } plot(df$x,vect,ylim=c(0,1),xlim=c(-5,5),type="l")

f <- approxfun(df\$x, vect, yleft = 0, yright = 0)
integrate(f, -Inf, Inf)