DELTD (version 2.6.5)

Erlang: Estimated Density Values by Erlang kernel

Description

Estimated values for density by using Erlang Kernel.

Usage

Erlang(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

Erlang kernel is developed by Salha et al. (2014). They developed this asymmetrical kernal with its hazard function and also proved its asymtotic normality. $$K_{E(x,\frac{1}{h})} (y)=\frac{1}{\Gamma (1+\frac{1}{h})} \left[\frac{1}{x} (1+\frac{1}{h}) \right]^\frac{h+1}{h} y^\frac{1}{h} exp\left(-\frac{y}{x} (1+\frac{1}{h}) \right)$$

References

Salha, R. B.; Ahmed, E. S.; Alhoubi, I. M. 2014. Hazard rate function estimation ksing Erlang Kernel. Pure Mathematical Sciences 3 (4), 141<U+2013>152.

See Also

For further MSE by using other kernels see BS, Gamma and LN. For plotting these estimated values plot.Erlang and for calculating MSE by using Erlang Kernel mseEr.

Examples

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