DEEVD (version 1.2.1)

Weibull: Estimated Density Values by Weibull kernel

Description

Estimated Kernel density values by using Weibull Kernel.

Usage

Weibull(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 Weibull kernel is developed by Salha et al. (2014). They used it to nonparametric estimation of the probability density function (pdf) and the hazard rate function for independent and identically distributed (iid) data. Weibull Kernel is $$ K_w\left( x, \frac{1}{h}\right)(t) =\frac{\Gamma(1+h)}{hx}\left[ \frac{t\Gamma(1+h)}{x}\right] ^{\frac{1}{h}-1} exp\left( -\left( \frac{t\Gamma(1+h)}{x}\right) ^\frac{1}{h}\right)$$

References

Salha, R. B., El Shekh Ahmed, H. I., & Alhoubi, I. M. 2014. Hazard Rate Function Estimation Using Weibull Kernel. Open Journal of Statistics 4 (08), 650-661.

See Also

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

Examples

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