Graphical methods for assessing normality

In the video, you learned how to create a histogram with 20 buckets that represents the probability density of the FTSE data, as well as how to add a normal distribution to the existing plot as a red line:

> hist(ftse, nclass = 20, probability = TRUE)
> lines(ftse, dnorm(ftse, mean = mu, sd = sigma), col = "red")

As you can see, dnorm(x, mean, sd) calculates the probability density function (PDF) of the data x with the calculated sample mean and standard deviation; this is known as the method-of-moments.

Finally, to calculate an estimate of the density of data x, use density(x). This creates a so-called kernel-density estimate (KDE) using a non-parametric method that makes no assumptions about the underlying distribution.

The various plots suggest that the data are heavier tailed than normal, although you will learn about better graphical and numerical tests in future exercises.

In this exercise, you will fit a normal distribution to the log-returns of the Dow Jones index for 2008-2009 and compare the data with the fitted distribution using a histogram and a density plot. The object djx containing Dow Jones data is loaded into your workspace.

This exercise is part of the course

Quantitative Risk Management in R

View Course

Exercise instructions

Calculate the average and standard deviation (sd()) of the djx data and assign to mu and sigma, respectively.
Plot a histogram of djx with 20 buckets that represents a probability density of the data.
Fill in the lines() and dnorm() functions to add the normal density curve for djx as a red line to the histogram.
Plot a kernel-density estimate for djx using density().
Use the same lines() command as above to add the normal density curve for djx as a red line to the KDE.

Hands-on interactive exercise

Have a go at this exercise by completing this sample code.

# Calculate average and standard deviation of djx
mu <- ___
sigma <- ___

# Plot histogram of djx
___(___)

# Add the normal density as a red line to histogram
lines(___, dnorm(___), col = ___)

# Plot non-parametric KDE of djx
___(___)

# Add the normal density as red line to KDE
lines(___, dnorm(___), col = ___)

Edit and Run Code