DEEVD (version 1.2.1)

Gumbel: Estimated Density Values by Gumbel kernel

Description

Estimated Kernel density values by using Gumbel Kernel.

Usage

Gumbel(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 Gumbel kernel is developed by Khan and Akbar (2020). They provided evidence that performance of their proposed is better then Weibull kernel especially when data belongs to family of extreme distributions. Gumbel Kernel is $$K_{Gumbel(x, \sqrt{h})}(j)=\frac{1}{\sqrt{h}}exp-\left( \frac{j-x}{\sqrt{h}} +exp\left( \frac{j-x}{\sqrt{h}}\right) \right)$$

References

Khan, J. A.; Akbar, A. Density Estimation by Gumbel Kernel. 2020. Working paper, Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.

See Also

For esitimated values by Weibull kernel see Weibull. Further, for plot and MSE by Gumbel kernel see plot.Gumbel and msegumbel, respectively.

Examples

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