AsyK (version 1.5.5)

RIG: 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)

Value

x

grid points

y

estimated values of density

Arguments

x

scheme for generating grid points

y

a numeric vector of positive values.

k

gird points.

h

the bandwidth

Author

Javaria Ahmad Khan, Atif Akbar.

Details

Scaillet 2003. proposed Reciprocal Inverse Gaussian kerenl. He claimed that his proposed kernel share the same properties as those of gamma kernel estimator. $$K_{RIG \left( \ln{ax}4\ln {(\frac{1}{h})} \right)}(y)=\frac{1}{\sqrt {2\pi y}} exp\left[-\frac{x-h}{2h} \left(\frac{y}{x-h}-2+\frac{x-h}{y}\right)\right]$$

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)

if (FALSE) {
##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)
}
#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)