## Plot density function in R

To create a density plot in R you can plot the object created with the R `density`

function, that will plot a density curve in a new R window. You can also overlay the density curve over an R histogram with the `lines`

function.

`set.seed(1234) # Generate data x <- rnorm(500)`

`par(mfrow = c(1, 2)) # Create a histogram hist(x, freq = FALSE, main = "Histogram and density") # Calculate density dx <- density(x) # Add density lines(dx, lwd = 2, col = "red") # Plot the density without histogram plot(dx, lwd = 2, col = "red", main = "Density") # Add the data-poins with noise in the X-axis rug(jitter(x))`

The result is the empirical density function. An alternative to create the empirical probability density function in R is the `epdfPlot`

function of the `EnvStats`

package. With this function, you can pass the numerical vector directly as a parameter.

`# Equivalent alternative with EnvStats package # install.packages("EnvStats") library(EnvStats) epdfPlot(x, epdf.col = "red")`

## Kernel density bandwidth selection

When you plot a probability density function in R you plot a kernel density estimate. The kernel density plot is a non-parametric approach that needs a bandwidth to be chosen. You can set the bandwidth with the `bw`

argument of the `density`

function.

In general, a big bandwidth will oversmooth the density curve, and a small one will undersmooth (overfit) the kernel density estimation in R. In the following code block you will find an example describing this issue.

`par(mfrow = c(1, 2)) # Big bandwidth plot(density(x, bw = 20), lwd = 2, col = "red", main = "Too big bandwidth") # Small bandwidth plot(density(x, bw = 0.05), lwd = 2, col = "red", main = "Too small bandwidth")`

Equivalently, you can pass arguments of the `density`

function to `epdfPlot`

within a list as parameter of the `density.arg.list`

argument. In this case, we are passing the `bw`

argument of the `density`

function.

`# Equivalent alternative with EnvStats package epdfPlot(x, epdf.col = "red", density.arg.list = list(bw = 0.05), main = "Too small bandwidth")`

The literature of kernel density bandwidth selection is wide. However, there are three main commonly used approaches to select the parameter:

- By default, the
`density`

function uses the rule of thumb approach - Using the plug-in methodology created by Sheather and Jones (1991).
- Using the cross-validation approach.

The following code shows how to implement each method:

`par(mfrow = c(1, 3)) # Rule of thumb plot(density(x), main = "Rule of thumb", cex.lab = 1.5, cex.main = 1.75, lwd = 2) # Unbiased cross validation plot(density(x, bw = bw.ucv(x)), col = 2, # Same as: bw = "UCV" main = "Cross-validation", cex.lab = 1.5, cex.main = 1.75, lwd = 2) # Plug-in plot(density(x, bw = bw.SJ(x)), col = 4, # Same as: bw = "SJ" main = "Plug-in bandwidth selection", cex.lab = 1.5, cex.main = 1.75, lwd = 2)`

You can also change the kernel with the `kernel`

argument, that will default to Gaussian. Although we won’t go into more details, the available kernels are `"gaussian"`

, `"epanechnikov"`

, `"rectangular"`

, `"triangular`

“, `"biweight"`

, `"cosine"`

and `"optcosine"`

. The selection will depend on the data you are working with.

## Multiple density curves in one plot

With the `lines`

function you can plot multiple density curves in R. You just need to plot a density in R and add all the new curves you want.

`par(mfrow = c(1, 1)) plot(dx, lwd = 2, col = "red", main = "Multiple curves", xlab = "") set.seed(2) y <- rnorm(500) + 1 dy <- density(y) lines(dy, col = "blue", lwd = 2)`

However, you may have noticed that the blue curve is cropped on the right side. To fix this, you can set `xlim`

and `ylim`

arguments as a vector containing the corresponding minimum and maximum axis values of the densities you would like to plot.

`plot(dx, lwd = 2, col = "red", main = "Multiple curves with correct axis limits", xlab = "", xlim = c(min(dx$x, dy$x), c(max(dx$x, dy$x))), # Min and Max X-axis limits ylim = c(min(dx$y, dy$y), c(max(dx$y, dy$y)))) # Min and Max Y-axis limits lines(dy, col = "blue", lwd = 2)`

`xlimand`

`ylimarguments of the`

`plotfunction, because the plot limits will default to the limits of the main curve.`

### Density comparison chart in R

There are several ways to compare densities. One approach is to use the `densityPlot`

function of the `car`

package. This function creates non-parametric density estimates conditioned by a factor, if specified. Type `?densityPlot`

for additional information.

`# Sample groups set.seed(1) groups <- factor(sample(c(1, 2), 100, replace = TRUE)) variable <- numeric(100) # Group 1: mean 3 variable[groups == 1] <- rnorm(length(variable[groups == 1]), 3) # Group 2: mean 0 variable[groups == 2] <- rnorm(length(variable[groups == 2]))`

`# Comparing densities by group # install.packages("car") library(car) densityPlot(variable, groups)`

Other alternative is to use the `sm.density.compare`

function of the `sm`

library, that compares the densities in a permutation test of equality.

`# install.packages("sm") library(sm) sm.density.compare(variable, groups) legend("topleft", levels(groups), col = 2:4, lty = 1:2)`

## Fill area under density curves

In base R you can use the `polygon`

function to fill the area under the density curve. If you use the `rgb`

function in the `col`

argument instead using a normal color, you can set the transparency of the area of the density plot with the `alpha`

argument, that goes from 0 to all transparency to 1, for a total opaque color.

`par(mfrow = c(1, 2)) #----------------------- # Shade area under curve #----------------------- plot(dx, lwd = 2, main = "", xlab = "", col = "red", xlim = c(-4, 6), ylim = c(0, 0.5)) polygon(dx, col = "red") polygon(dx$x, dx$y, col = "red") # Equivalent set.seed(2) y <- rnorm(500) + 2 dy <- density(y) lines(dy, lwd = 2, col = "blue") polygon(dy, col = "blue") #----------------------------------------- # Shade area under curve with transparency #----------------------------------------- plot(dx, lwd = 2, main = "", xlab = "", col = "red", xlim = c(-4, 6), ylim = c(0, 0.5)) polygon(dx, col = rgb(1, 0, 0, alpha = 0.5)) lines(dy, lwd = 2, col = "blue") polygon(dy, col = rgb(0, 0, 1, alpha = 0.5))`

If you are using the `EnvStats`

package, you can add the color setting with the `curve.fill.col`

argument of the `epdfPlot`

function.

`# Equivalent alternative with EnvStats package library(EnvStats) epdfPlot(x, # Vector with data curve.fill = TRUE, # Fill the area curve.fill.col = rgb(1, 0, 0, alpha = 0.5), # Area color epdf.col = "red") # Line color epdfPlot(y, curve.fill = TRUE, curve.fill.col = rgb(0, 0, 1, alpha = 0.5), epdf.col = "blue", add = TRUE) # Add the density over the previous plot`

You can also fill only a specific area under the curve. In the following example we show you, for instance, how to fill the curve for values of `x`

greater than 0.

`par(mfrow = c(1, 1)) plot(dx, lwd = 2, main = "Density", col = "red") polygon(c(dx$x[dx$x >= 0], 0), c(dx$y[dx$x >= 0], 0), col = rgb(1, 0, 0, alpha = 0.5), border = "red", main = "")`

## Density plot with ggplot2

You can create a density plot with R `ggplot2`

package. For that purpose, you can make use of the `ggplot`

and `geom_density`

functions as follows:

`library(ggplot2) df <- data.frame(x = x) ggplot(df, aes(x = x)) + geom_density(color = "red", # Curve color fill = "red", # Area color alpha = 0.5) # Area transparency`

If you want to add more curves, you can set the X axis limits with `xlim`

function and add a legend with the `scale_fill_discrete`

as follows:

`df <- data.frame(x = x, y = y) df <- stack(df) dx <- density(x) dy <- density(y) ggplot(df, aes(x = values, fill = ind)) + geom_density(alpha = 0.5) + # Densities with transparency xlim(c(min(dx$x, dy$x), # X-axis limits c(max(dx$x, dy$x)))) + scale_fill_discrete(name = "Legend title", # Change legend title labels = c("A", "B")) # + # Change default legend labels # theme(legend.position = "none") # Delete legend # Equivalent ggplot(df, aes(x = values)) + geom_density(aes(group = ind, fill = ind), alpha = 0.5) + xlim(c(min(dx$x, dy$x), c(max(dx$x, dy$x)))) + scale_fill_discrete(name = "Legend title", labels = c("A", "B"))`