DELTD (version 2.6.5)

BS: Estimated Density Values by Birnbaum-Saunders kernel

Description

Estimated Values by using Birnbaum-Saunders Kernel.

Usage

BS(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 Birnbaum-Saunders kernel is developed by Jin and Kawczak (2003). They claimed that performance of their developed kernel is better near the boundary points in terms of boundary reduction. $$K_{BS(h^\frac{1}{2},x)} (y)=\frac{1}{2\sqrt 2 \pi h} \left(\sqrt \frac{1}{xy} +\sqrt\frac{x}{y^3}\right)exp\left(-\frac{1}{2h}\left(\frac{y}{x}-2+\frac{x}{y}\right)\right)$$

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 LN. To plot the density by using BS kernel plot.BS and to calculate MSE by using Birnbaum-Saunders Kernel mseBS.

Examples

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