kcdf: Estimation of the cumulative distribution function using...

In ialmodovar/SynClustR: Syncytial Clustering Algorithms in R

Estimation of the cumulative distribution function using kernel smoothing

Description

Perform kernel estimation of the cumulative distribution function.

Usage

 kcdf(x, b = NULL, kernel = "RIG", xgrid = NULL, m = 100, inv.roles = FALSE) 

Arguments

x	A vector (univariate). Default is use of asymmetric kernel defined in the positive real line. These kernel are Reciprocal Inverse Gaussian (RIG), Gamma and Gamma with inverse roles. If the vector contain at least a negative number will use Gaussian kernel.
b	Smoothing parameter (Bandwidth). Default is NULL and will estimate the bandwith using a rule-of-thumb that minimize the mean integrated squared error.
kernel	Choice of the kernel to be use in the smooth estimation. Default is Reciprocal Inverse Gaussian (RIG), other choices are Gamma kernel, Gamma kernel with inverse roles and Gaussian kernel.
xgrid	Range of grid values that will be evaluated.
m	Maximum number of grid.
inv.roles	Only for Gamma kernel estimation. Default is FALSE, which means kde will be perform using Chen (2000), if TRUE will use Jeon and Kim (2013) with inverse roles.

Details

Default is use of asymmetric kernel defined in the positive real line. These kernel are Reciprocal Inverse Gaussian (RIG), Gamma and Gamma with inverse roles. If the vector contain at least a negative number will use Gaussian kernel

Author(s)

Israel Almodovar-Rivera.

References

Chen, S. X. (2000). Probability density function estimation using gamma kernels. Annals of the Institute of Statistical Mathematics, 52(3), 471-480.

Jeon, Y., & Kim, J. H. (2013). A gamma kernel density estimation for insurance loss data. Insurance: Mathematics and Economics, 53(3), 569-579.

Scaillet, O. (2004). Density estimation using inverse and reciprocal inverse Gaussian kernels. Nonparametric statistics, 16(1-2), 217-226.

Examples

set.seed(787)
## gamma(5/2,2) = chisquared with 5 degrees
x <- rgamma(n = 500,shape= 5/2,scale = 2)
xg <- sort(x)
## reciprocal inverse gaussian
F.rig <- kcdf(x, kernel = "RIG",xgrid=xg)
## Gamma kernel of Chen (2000)
F.gamma1 <- kcdf(x, kernel = "gamma",xgrid=xg)
## Gamma kernel of Jeon and Kim (2013)
F.gamma2 <- kcdf(x, kernel = "gamma",inv.roles=TRUE,xgrid=xg)
## Gaussian kernel
F.gaussian <- kcdf(x,kernel="gaussian",xgrid=xg)
## True cdf
F.true <- pgamma(sort(x), shape = 5/2,scale= 2)
## sort data only for display purposes
plot(xg,F.true,col="black",type="l",lwd=2)
lines(xg,F.rig$Fhat,col="red",lwd=2)
lines(xg,F.gamma1$Fhat,col="blue",lwd = 2)
lines(xg,F.gamma2$Fhat,col="orange",lwd = 2)
lines(xg,F.gaussian$Fhat,col="green",lwd=2)
legend("bottomright",col=c("black","red","blue","orange","green"),lty=rep(1,5),lwd=rep(2,5),
legend=c("True","RIG kernel","Gamma kernel","Gamma kernel with inverse roles","Gaussian kernel"))

ialmodovar/SynClustR documentation built on July 7, 2023, 12:18 a.m.