Library

library(ggplot2)

Data

set.seed(77)  # guarantees identical random data when 'rnorm' command is repeated
dat = data.frame(X = rnorm(300, mean = 2, sd = 3))   
str(dat)
## 'data.frame':    300 obs. of  1 variable:
##  $ X: num  0.351 5.273 3.919 5.128 2.509 ...
head(dat)
##          X
## 1 0.351086
## 2 5.273162
## 3 3.919333
## 4 5.127728
## 5 2.509110
## 6 5.413401

Histogram

A histogram with counts (not normalised to 1):

ggplot(dat, aes(x = X)) +
  geom_histogram(color = "black", fill = "steelblue", binwidth = 0.7) +
  labs(x = "x", y = "Frequency") +
  ggtitle("Histogram of random variable X") +
  theme_minimal()

More explanations on this good site.

Histogram with density curve

Now, we use bins = … instead of binwidth = …, i.e. we fix the number of bins, not their width:

ggplot(dat, aes(x = X, y = after_stat(density))) +     
  geom_histogram(aes(y = after_stat(density)), color = "black", fill = "steelblue", bins = 30, alpha = 0.7) +
  labs(x = "", y = "Frequency") +                               # axis labels, we leave the x-axis empty here
  ggtitle("Histogram of the random variable X") +
  geom_density(color = "red", linewidth = 1.0, alpha = 0.5) +   # add density curve
  theme_minimal()

Note the y = after_stat(density). This normalises to area 1 !

When using ggplot for the density plot, there is no need to call the density() function. However, if we don’t, we cannot use the density() function output for further calculations!

Create and plot the CDF

We can use the function ecdf to estimate a cumulative distribution function from measured data. In base R, we call this function and plot the CDF afterwards:

CDF <- ecdf(dat$X)  # get the CDF 
str(CDF)            
## function (v)  
##  - attr(*, "class")= chr [1:3] "ecdf" "stepfun" "function"
##  - attr(*, "call")= language ecdf(dat$X)
plot(CDF, main = "CDF", xlab = "x", ylab = "F(x)", col = "blue", cex = 0.5, font.main = 1)

The CDF object represents a function, but the following plot command “knows” how to treat it.

When using ggplot, there is no need to call ecdf explicitely. The CDF is calculated internally when the layer stat_ecdf() is included. The disadvantage is, that we don’t have the CDF data for further calculations.

ggplot(dat, aes(x = X)) + stat_ecdf(col = "red")

Again, more details here.

Note that all code snippets are designed for comprehensibility, not for efficiency!


uwe.menzel@matstat.org