LogN {DELTD}

Estimate Density Values by Lognormal kernel

Description

The LogN estimate Values of density by using Lognormal Kernel.The Lognomal kernel is 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]

Usage

LogN(x = NULL, y, k = NULL, h = NULL)

Arguments

x

scheme for generating grid points

y

a numeric vector of positive values.

k

gird points.

h

the bandwidth

Details

see the details in the BS.

Value

x

grid points

y

estimated values of density

Author(s)

Javaria Ahmad Khan, Atif Akbar.

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, 103-124.

See Also

For further kernels see Beta, Erlang, Gamma and BS. To plot its density see plot.LogN and to calculate MSE use mse.

Examples

## Data: Simulated or real data can be used
## Number of grid points "k" should be at least equal to the data size.
## If user defines the generating scheme of grid points then length
## of grid points should be equal or greater than "k", Otherwise NA will be produced.
y <- rweibull(350, 1)
xx <- seq(0.001, max(y), length = 500)
h <- 2
den <- LogN(x = xx, y = y, k = 200, h = h)

##If scheme for generating grid points is unknown
n <- 1000
y <- abs(rlogis(n, location = 0, scale = 1))
h <- 3
LogN(y = y, k = 90, h = h)

## Not run: 
##If user do not mention the number of grid points
y <- rweibull(350, 1)
xx <- seq(0.00001, max(y), 500)

#any bandwidth can be used
require(ks)
h <- hscv(y)   #Smooth cross validation bandwidth
LogN(x = xx, y = y, h = h)

## End(Not run)

## Not run: 
#if both scheme and number of grid points are missing then function generate NA
n <- 1000
y <- abs(rlogis(n, location = 0, scale = 1))
band = 3
LogN(y = y, h = band)

## End(Not run)

#if bandwidth is missing
y <- rweibull(350, 1)
xx <- seq(0.001, 100, length = 500)
LogN(x = xx, y = y, k = 90)