RIG {AsyK}

Estimated Density Values by Reciprocal Inverse Gaussian kernel

Description

Estimated Kernel density values by using Reciprocal Inverse Gaussian Kernel.

Usage

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 \left( \ln{ax}4\ln {(\frac{1}{h})} \right)}(y)=\frac{1}{\sqrt {2\pi y}} exp\left[-\frac{x-h}{2h} \left(\frac{y}{x-h}-2+\frac{x-h}{y}\right)\right]

Value

x

grid points

y

estimated values of density

Author(s)

Javaria Ahmad Khan, Atif Akbar.

References

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

See Also

To examine RIG density plot see plot.RIG and for Mean Squared Error mse. Similarly, for Laplace kernel Laplace.

Examples

#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)