# Weibull: Estimated Density Values by Weibull kernel In DEEVD: Density Estimation by Extreme Value Distributions

## Description

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≤ft( x, \frac{1}{h}\right)(t) =\frac{Γ(1+h)}{hx}≤ft[ \frac{tΓ(1+h)}{x}\right] ^{\frac{1}{h}-1} exp≤ft( -≤ft( \frac{tΓ(1+h)}{x}\right) ^\frac{1}{h}\right)

## Usage

 1 Weibull(x = NULL, y, k = NULL, h = NULL) 

## Arguments

 x scheme for generating grid points y a numeric vector of positive values k number of gird points h the bandwidth

## Details

see the details in the Gumbel

## Value

 x grid points y estimated values of density

## 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. Silverman, B. W. 1986. Density Estimation. Chapman & Hall/ CRC, London.

For Gumbel kernel see Gumbel. To plot its density see plot.Weibull and to calculate MSE mse.
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 #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 produduced. y <- rexp(100, 1) xx <- seq(min(y) + 0.05, max(y), length = 100) h <- 2 den <- Weibull(x = xx, y = y, k = 200, h = h) ##If scheme for generating gridpoints is unknown y <- rexp(50, 1) h <- 3 den <- Weibull(y = y, k = 90, h = h) ##If user do not mention the number of grid points y <- rexp(23, 1) xx <- seq(min(y) + 0.05, max(y), length = 90) ## Not run: #any bandwidth can be used require(KernSmooth) h <- dpik(y) den <- Weibull(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 <- Weibull(x = xx, y = y, k = 90)