# Estimate Density Values by Lognormal kernel 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 [REMOVE_ME]$$ K_{LN(\ln(x),4\ln(1+h))}=\frac{1}{\sqrt{( 8\pi \ln(1+h))} y)} exp\left[-\frac{(\ln(y)-\ln(x))^2}{(8\ln(1+h))}\right] [REMOVE_ME_2]$$ ```r 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 ## Returns - **x**: grid points - **y**: estimated values of density ## 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 $$ K_{LN(\ln(x),4\ln(1+h))}=\frac{1}{\sqrt{( 8\pi \ln(1+h))} y)} exp\left[-\frac{(\ln(y)-\ln(x))^2}{(8\ln(1+h))}\right] $$ ## Details see the details in the `BS`. ## Examples ```r ## 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) ``` ## 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`. ## Author(s) Javaria Ahmad Khan, Atif Akbar.

LogN function