# x_bimodal: Understanding kernel smoothing through a simulated dataset In ACSWR: A Companion Package for the Book "A Course in Statistics with R"

## Description

This is a simulated dataset with two modes at -2 and 2 and we have 400 observations.

## Usage

 `1` ```data(x_bimodal) ```

## Format

The format is: num [1:400] -4.68 -4.19 -4.05 -4.04 -4.02 ...

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23``` ```data(x_bimodal) h <- 0.5; n <- length(x_bimodal) dens_unif <- NULL; dens_triangle <- NULL; dens_epanechnikov <- NULL dens_biweight <- NULL; dens_triweight <- NULL; dens_gaussian <- NULL for(i in 1:n) { u <- (x_bimodal[i]-x_bimodal)/h xlogical <- (u>-1 & u <= 1) dens_unif[i] <- (1/(n*h))*(sum(xlogical)/2) dens_triangle[i] <- (1/(n*h))*(sum(xlogical*(1-abs(u)))) dens_epanechnikov[i] <- (1/(n*h))*(sum(3*xlogical*(1-u^2)/4)) dens_biweight[i] <- (1/(n*h))*(15*sum(xlogical*(1-u^2)^2/16)) dens_triweight[i] <- (1/(n*h))*(35*sum(xlogical*(1-u^2)^3/32)) dens_gaussian[i] <- (1/(n*h))*(sum(exp(-u^2/2)/sqrt(2*pi))) } plot(x_bimodal,dens_unif,"l",ylim=c(0,.25),xlim=c(-5,7),xlab="x", ylab="Density",main="B: Applying Kernel Smoothing") points(x_bimodal,dens_triangle,"l",col="red") points(x_bimodal,dens_epanechnikov,"l",col="green") points(x_bimodal,dens_biweight,"l",col="blue") points(x_bimodal,dens_triweight,"l",col="yellow") points(x_bimodal,dens_gaussian,"l",col="orange") legend(4,.23,legend=c("rectangular","triangular","epanechnikov","biweight", "gaussian"),col=c("black","red","green","blue","orange"),lty=1) ```

ACSWR documentation built on May 2, 2019, 6:53 a.m.