# RIG: Estimated Density Values by Reciprocal Inverse Gaussian... In AsyK: Kernel Density Estimation

## Description

Estimated Kernel density values by using Reciprocal Inverse Gaussian Kernel.

## Usage

 1 RIG(x = NULL, y, k = NULL, h = NULL) 

## Arguments

 x scheme for generating grid points y a numeric vector of positive values. k gird points. h the bandwidth

## Details

Scaillet 2003. proposed Reciprocal Inverse Gaussian kerenl. He claimed that his proposed kernel share the same properties as those of gamma kernel estimator.

K_{RIG ≤ft( \ln{ax}4\ln {(\frac{1}{h})} \right)}(y)=\frac{1}{√ {2π y}} exp≤ft[-\frac{x-h}{2h} ≤ft(\frac{y}{x-h}-2+\frac{x-h}{y}\right)\right]

## Value

 x grid points y estimated values of density

## References

Scaillet, O. 2004. Density estimation using inverse and reciprocal inverse Gaussian kernels. Nonparametric Statistics, 16, 217-226.

To examine RIG density plot see plot.RIG and for Mean Squared Error mse. Similarly, for Laplace kernel Laplace.
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 #Data can be simulated or real data ## Number of grid points "k" should be at least equal to the data size. ### If user define the generating scheme of gridpoints than number of gridpoints should ####be equal or greater than "k" ###### otherwise NA will be produced. y <- rexp(100, 1) xx <- seq(min(y) + 0.05, max(y), length = 100) h <- 2 den <- RIG(x = xx, y = y, k = 200, h = h) ##If scheme for generating gridpoints is unknown y <- rexp(50, 1) h <- 3 den <- RIG(y = y, k = 90, h = h) ## Not run: ##If user do not mention the number of grid points y <- rexp(23, 1) xx <- seq(min(y) + 0.05, max(y), length = 90) #any bandwidth can be used require(KernSmooth) h <- dpik(y) den <- RIG(x = xx, y = y, h = h) ## End(Not run) #if bandwidth is missing y <- rexp(100, 1) xx <- seq(min(y) + 0.05, max(y), length = 100) den <- RIG(x = xx, y = y, k = 90)