Module 4: Bivariate Displays

(The attached PDF file have better formatting.)

Homework Assignment: quantile comparison plots

Quantile comparison plots are discussed in Module 3 and are used later in the text. This homework assignment discusses quantile comparison plots, not bivariate displays

We compare quantile comparison plots for two distributions:

           Figure 3.9 on page 37: A t-distribution with 3 degrees of freedom.

           Figure 3.8 on page 37: A ÷-squared distribution with 2 degrees of freedom.

Below is a quantile comparison plot for 1,000 random draws from a t-distribution with 3 degrees of freedom.

The quantile comparison plot for a t-distribution with 2 degrees of freedom is shaped like an S-curve.

A.     At the upper tail, are values more or less extreme than in a normal distribution?

B.     At the lower tail, are values more or less extreme than in a normal distribution?

C.    Is the t-distribution with 2 degrees of freedom (i) symmetric thin-tailed, (ii) symmetric thick-tailed, (iii) positively skewed, or (iv) negatively skewed?

Below is a quantile comparison plot for 1,000 random draws from a χ-squared distribution with 2 degrees of freedom.

The quantile comparison plot for a χ-squared distribution with 2 degrees of freedom is shaped like a convex banana.