Fox Module 4: Bivariate Displays HW


Fox Module 4: Bivariate Displays HW

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NEAS
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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?

 

 


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wangxy
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Please define extreme. I would really like to know it as well. I am guessing if the points lie above the comparison line, it is more extreme, otherwise it would be less extreme. Am I correct? Text book Page 37 Figure 3.9 defines heavy tail, I am guessing this is also symmetric thick tail? then should the symmetric thin tail be opposite of what is draw in figure 3.9???? (below comparison line at higher values and above comparison line at lower values????)

[NEAS: Thick tailed distributions (heavy tailed, long tailed, fat tailed) have many definitions. This course refers to thick tailed as any distribution with thicker tails than the normal distribution. A normal distribution has a straight line for a quantile comparison plot. A thin or thick tailed distribution has points that deviate from the straight line, but in opposite directions. Consider the lognormal distribution, which is thick tailed on the right but thin tailed on the left (since values are bounded by zero). Examine the quantile comparison plot: what does it mean that the points are above or below the straight line?]


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