# Density plot in R

The probability density function of a vector x, denoted by f(x) describes the probability of the variable taking certain value. The empirical probability density function is a smoothed version of the histogram. This is also known as the Parzen–Rosenblatt estimator or kernel estimator. You can make a density plot in R in very simple steps we will show you in this tutorial, so at the end of the reading you will know how to plot a density in R or in RStudio.

## 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)

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:

1. By default, the `density` function uses the rule of thumb approach
2. Using the plug-in methodology created by Sheather and Jones (1991).
3. 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)``````

The selection of the bandwidth parameter will depend on the data you are working with or the objectives of your study. Choose the bandwidth approach carefully.

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)``````

When plotting multiple lines, it is a good practice to set the axis limits with the `xlim` and `ylim` arguments of the `plot` function, 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) ``````

Note that the density graphs are different due to the methods to compute the densities are different. Check the bibliography of each method, available in the documentation of each function, for additional details.

## 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))

#-----------------------
#-----------------------

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",

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"))``````