| Title: | Kernel Density Estimation |
|---|---|
| Description: | A collection of functions related to density estimation by using Chen's (2000) idea. Mean Squared Errors (MSE) are calculated for estimated curves. For this purpose, R functions allow the distribution to be Gamma, Exponential or Weibull. For details see Chen (2000), Scaillet (2004) <doi:10.1080/10485250310001624819> and Khan and Akbar. |
| Authors: | Javaria Ahmad Khan, Atif Akbar. |
| Maintainer: | Javaria Ahmad Khan <[email protected]> |
| License: | GPL-2 |
| Version: | 1.5.5 |
| Built: | 2025-02-14 04:10:40 UTC |
| Source: | https://github.com/cran/AsyK |
A collection of functions related to density estimation by using Chen's (2000) idea. For observing estimated values see Laplace and RIG. Plots by using these kernels can be drawn by plot.Laplace and plot.RIG. Mean squared errors (MSE) can be calculated by mse.
Here we also present a normal scale rule bandwidth which is given by Silverman (1986) for non-normal data.
Kernel Density Estimation
Javaria Ahmad Khan, Atif Akbar.
Useful links:
Estimated Kernel density values by using Laplace Kernel.
Laplace(x = NULL, y, k = NULL, h = NULL)Laplace(x = NULL, y, k = NULL, h = NULL)
x |
scheme for generating grid points |
y |
a numeric vector of positive values. |
k |
gird points. |
h |
the bandwidth |
Laplace kernel is developed by Khan and Akbar. Kernel is developed by using Chen's idea. Laplace kernel is;
x |
grid points |
y |
estimated values of density |
Javaria Ahmad Khan, Atif Akbar.
Khan, J. A.; Akbar, A. Density Estimation by Laplace Kernel. Working paper, Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
To examine Laplace density plot see plot.Laplace and for Mean Squared Error mse. Similarly, for RIG kernel RIG.
#Data can be simulated or real data ## Number of grid points "k" should be at least equal to the data size. ### If user define the generating scheme of gridpoints than number of gridpoints should ####be equal or greater than "k" ###### otherwise NA will be produced. y <- rexp(100, 1) xx <- seq(min(y) + 0.05, max(y), length = 100) h <- 2 den <- Laplace(x = xx, y = y, k = 200, h = h) ##If scheme for generating gridpoints is unknown y <- rexp(50, 1) h <- 3 den <- Laplace(y = y, k = 90, h = h) ##If user do not mention the number of grid points y <- rexp(23, 1) xx <- seq(min(y) + 0.05, max(y), length = 90) ## Not run: #any bandwidth can be used require(KernSmooth) h <- dpik(y) den <- Laplace(x = xx, y = y, h = h) ## End(Not run) #if bandwidth is missing y <- rexp(100, 1) xx <- seq(min(y) + 0.05, max(y), length = 100) den <- Laplace(x = xx, y = y, k = 90)#Data can be simulated or real data ## Number of grid points "k" should be at least equal to the data size. ### If user define the generating scheme of gridpoints than number of gridpoints should ####be equal or greater than "k" ###### otherwise NA will be produced. y <- rexp(100, 1) xx <- seq(min(y) + 0.05, max(y), length = 100) h <- 2 den <- Laplace(x = xx, y = y, k = 200, h = h) ##If scheme for generating gridpoints is unknown y <- rexp(50, 1) h <- 3 den <- Laplace(y = y, k = 90, h = h) ##If user do not mention the number of grid points y <- rexp(23, 1) xx <- seq(min(y) + 0.05, max(y), length = 90) ## Not run: #any bandwidth can be used require(KernSmooth) h <- dpik(y) den <- Laplace(x = xx, y = y, h = h) ## End(Not run) #if bandwidth is missing y <- rexp(100, 1) xx <- seq(min(y) + 0.05, max(y), length = 100) den <- Laplace(x = xx, y = y, k = 90)
This function calculates the mean squared error (MSE) by using user specified kernel.This function is same as provided in package "DELTD". For details see https://CRAN.R-project.org/package=DELTD.
MSE(kernel, type)MSE(kernel, type)
kernel |
type of kernel which is to be used |
type |
mention distribution of vector.If exponential distribution then use |
Mean Squared Error (MSE)
Javaria Ahmad Khan, Atif Akbar.
https://CRAN.R-project.org/package=DELTD
Calculate Bandwidth proposed by Silverman for non-normal data.
NSR(y)NSR(y)
y |
a numeric vector of positive values. |
h
Javaria Ahmad Khan, Atif Akbar.
Silverman, B. W. 1986. Density Estimation. Chapman & Hall/ CRC, London.
y <- rexp(10, 1) NSR(y)y <- rexp(10, 1) NSR(y)
Plot density by using Laplace Kernel.
## S3 method for class 'Laplace' plot(x, ...)## S3 method for class 'Laplace' plot(x, ...)
x |
an object of class "Laplace" |
... |
Not presently used in this implementation |
nothing
Javaria Ahmad Khan, Atif Akbar.
Khan, J. A.; Akbar, A. Density Estimation by Laplace Kernel. Working paper, Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan.
To examine Laplace estimated values for density see Laplace and for Mean Squared Error mse. Similarly, for plot of Laplace kernel plot.RIG.
y <- rexp(100, 1) h <- 0.79 * IQR(y) * length(y) ^ (-1/5) xx <- seq(min(y) + 0.05, max(y), length = 100) den <- Laplace(x = xx, y = y, k = 100, h = h) plot(den, type = "l") ##other details can also be added y <- rexp(100, 1) h <- 0.79 * IQR(y) * length(y) ^ (-1/5) den <- Laplace(x = xx, y = y, k = 100, h = h) plot(den, type = "s", ylab = "Density Function", lty = 1, xlab = "Time") ## To add true density along with estimated d1 <- density(y, bw = h) lines(d1, type = "p", col = "red") legend("topright", c("Real Density", "Density by RIG Kernel"), col = c("red", "black"), lty = c(1, 2))y <- rexp(100, 1) h <- 0.79 * IQR(y) * length(y) ^ (-1/5) xx <- seq(min(y) + 0.05, max(y), length = 100) den <- Laplace(x = xx, y = y, k = 100, h = h) plot(den, type = "l") ##other details can also be added y <- rexp(100, 1) h <- 0.79 * IQR(y) * length(y) ^ (-1/5) den <- Laplace(x = xx, y = y, k = 100, h = h) plot(den, type = "s", ylab = "Density Function", lty = 1, xlab = "Time") ## To add true density along with estimated d1 <- density(y, bw = h) lines(d1, type = "p", col = "red") legend("topright", c("Real Density", "Density by RIG Kernel"), col = c("red", "black"), lty = c(1, 2))
Plot density by using Reciprocal Inverse Gaussian Kernel.
## S3 method for class 'RIG' plot(x, ...)## S3 method for class 'RIG' plot(x, ...)
x |
an object of class "RIG" |
... |
Not presently used in this implementation |
nothing
Javaria Ahmad Khan, Atif Akbar.
Scaillet, O. 2004. Density estimation using inverse and reciprocal inverse Gaussian kernels. Nonparametric Statistics, 16, 217-226.
To examine RIG estimated values for density see RIG and for Mean Squared Error mse. Similarly, for plot of Laplace kernel plot.Laplace.
y <- rexp(200, 1) h <- 0.79 * IQR(y) * length(y) ^ (-1/5) xx <- seq(min(y) + 0.05, max(y), length = 200) den <- RIG(x = xx, y = y, k = 200, h = h) plot(den, type = "l") ##other details can also be added y <- rexp(200, 1) h <- 0.79 * IQR(y) * length(y) ^ (-1/5) den <- RIG(x = xx, y = y, k = 200, h = h) plot(den, type = "s", ylab = "Density Function", lty = 1, xlab = "Time") ## To add true density along with estimated d1 <- density(y, bw = h) lines(d1, type = "p", col = "red") legend("topright", c("Real Density", "Density by RIG Kernel"), col = c("red", "black"), lty = c(1, 2))y <- rexp(200, 1) h <- 0.79 * IQR(y) * length(y) ^ (-1/5) xx <- seq(min(y) + 0.05, max(y), length = 200) den <- RIG(x = xx, y = y, k = 200, h = h) plot(den, type = "l") ##other details can also be added y <- rexp(200, 1) h <- 0.79 * IQR(y) * length(y) ^ (-1/5) den <- RIG(x = xx, y = y, k = 200, h = h) plot(den, type = "s", ylab = "Density Function", lty = 1, xlab = "Time") ## To add true density along with estimated d1 <- density(y, bw = h) lines(d1, type = "p", col = "red") legend("topright", c("Real Density", "Density by RIG Kernel"), col = c("red", "black"), lty = c(1, 2))
Estimated Kernel density values by using Reciprocal Inverse Gaussian Kernel.
RIG(x = NULL, y, k = NULL, h = NULL)RIG(x = NULL, y, k = NULL, h = NULL)
x |
scheme for generating grid points |
y |
a numeric vector of positive values. |
k |
gird points. |
h |
the bandwidth |
Scaillet 2003. proposed Reciprocal Inverse Gaussian kerenl. He claimed that his proposed kernel share the same properties as those of gamma kernel estimator.
x |
grid points |
y |
estimated values of density |
Javaria Ahmad Khan, Atif Akbar.
Scaillet, O. 2004. Density estimation using inverse and reciprocal inverse Gaussian kernels. Nonparametric Statistics, 16, 217-226.
To examine RIG density plot see plot.RIG and for Mean Squared Error mse. Similarly, for Laplace kernel Laplace.
#Data can be simulated or real data ## Number of grid points "k" should be at least equal to the data size. ### If user define the generating scheme of gridpoints than number of gridpoints should ####be equal or greater than "k" ###### otherwise NA will be produced. y <- rexp(100, 1) xx <- seq(min(y) + 0.05, max(y), length = 100) h <- 2 den <- RIG(x = xx, y = y, k = 200, h = h) ##If scheme for generating gridpoints is unknown y <- rexp(50, 1) h <- 3 den <- RIG(y = y, k = 90, h = h) ## Not run: ##If user do not mention the number of grid points y <- rexp(23, 1) xx <- seq(min(y) + 0.05, max(y), length = 90) #any bandwidth can be used require(KernSmooth) h <- dpik(y) den <- RIG(x = xx, y = y, h = h) ## End(Not run) #if bandwidth is missing y <- rexp(100, 1) xx <- seq(min(y) + 0.05, max(y), length = 100) den <- RIG(x = xx, y = y, k = 90)#Data can be simulated or real data ## Number of grid points "k" should be at least equal to the data size. ### If user define the generating scheme of gridpoints than number of gridpoints should ####be equal or greater than "k" ###### otherwise NA will be produced. y <- rexp(100, 1) xx <- seq(min(y) + 0.05, max(y), length = 100) h <- 2 den <- RIG(x = xx, y = y, k = 200, h = h) ##If scheme for generating gridpoints is unknown y <- rexp(50, 1) h <- 3 den <- RIG(y = y, k = 90, h = h) ## Not run: ##If user do not mention the number of grid points y <- rexp(23, 1) xx <- seq(min(y) + 0.05, max(y), length = 90) #any bandwidth can be used require(KernSmooth) h <- dpik(y) den <- RIG(x = xx, y = y, h = h) ## End(Not run) #if bandwidth is missing y <- rexp(100, 1) xx <- seq(min(y) + 0.05, max(y), length = 100) den <- RIG(x = xx, y = y, k = 90)