DELTD (version 2.6.5)

Gamma: Estimated Density Values by Gamma kernel

Description

Estimated Kernel density values by using Gamma Kernel.

Usage

Gamma(y, k, h)

Arguments

y

a numeric vector of positive values.

k

gird points.

h

the bandwidth

Value

x

grid points

y

estimated values of density

Details

The Gamma kernel is developed by Chen (2000). He was first to introduce asymetrical kernels to control boundary Bias. Gamma Kernel is $$K_{Gam1( \frac{x}{h+1}, h)}(y) = \frac{y^ \frac{x}{h} exp(-\frac{y}{h})}{ \Gamma \frac{x}{(h+1)}h^{ \frac{x}{h+1}}}$$

References

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

See Also

For further kernels see Erlang, BS and LN. To plot its density see plot.Gamma and to calculate MSE by using Gamma Kernel mseGamma.

Examples

# NOT RUN {
y <- rexp(100,1)
h <- 0.79 * IQR(y) * length(y) ^ (-1/5)
Gamma(y,200,h)
# }