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.
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 a ÷-squared distribution with df = 2 (i) symmetric thin-tailed, (ii) symmetric thick-tailed, (iii) positively skewed, or (iv) negatively skewed?