DELTD (version 2.6.5)

LN: Estimated Density Values by Lognormal kernel

Description

Estimated Values of Density estimation by using Lognormal Kernel.

Usage

LN(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 Lognomal kernel is also developed by Jin and Kawczak (2003). For this too, they claimed that performance of their developed kernel is better near the boundary points in terms of boundary reduction. Lognormal Kernel is $$K_{LN(\ln(x),4\ln(1+h))}=\frac{1}{\sqrt{( 8\pi \ln(1+h))} y)} exp\left[-\frac{(\ln(y)-\ln(x))^2}{(8\ln(1+h))}\right]$$

References

Jin, X.; Kawczak, J. 2003. Birnbaum-Saunders & Lognormal kernel estimators for modeling durations in high frequency financial data. Annals of Economics and Finance 4, 103<U+2013>124.

See Also

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

Examples

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