Answer-first summary for fast verification
Answer: The tails of the empirical distribution are heavier than those of the reference distribution if the QQ plot has a steeper slope at its tails.
## Explanation **A is correct.** If the empirical distribution has heavier tails than the reference distribution, the QQ plot will have steeper slopes at its tails. Conversely, if the empirical distribution has lighter tails than the reference distribution, the QQ plot will have flatter slopes at its tails. **B is incorrect.** Outliers are easily identified on QQ plots due to the nature of the plotting, and this is one of the ways QQ plots are useful. QQ plots do not smooth the distribution by removing outliers. **C is incorrect.** Reference distributions that produce non-linear QQ plots can be dismissed from consideration as a good representative of the empirical data since data drawn from the reference distribution should produce a linear QQ plot. **D is incorrect.** The primary purpose of a QQ plot is to determine the proper reference distribution. One can see if there is skewness and kurtosis although it cannot be measured with a QQ plot. ## Key Learning Points - QQ plots compare quantiles of empirical data against quantiles of a reference distribution - Steeper slopes at tails indicate heavier tails in empirical distribution - Linear QQ plots suggest the reference distribution is appropriate - QQ plots help identify outliers and distribution characteristics - They are primarily used for distribution comparison, not direct measurement of skewness/kurtosis
Author: LeetQuiz .
Ultimate access to all questions.
A risk analyst is studying a series of graphs plotting the empirical distribution of a portfolio's profit and loss quantiles against the quantiles of different specified reference distributions. The analyst plans to use these QQ plots to gain insights into the properties of the empirical distribution of the portfolio's profits and losses. Which of the following statements is correct regarding QQ plots?
A
The tails of the empirical distribution are heavier than those of the reference distribution if the QQ plot has a steeper slope at its tails.
B
QQ plots are used to smooth the empirical distribution by removing outliers through the use of quantiles.
C
A distribution is considered a good reference distribution if data drawn from it produces a QQ plot that is non-linear in the central mass of the distribution.
D
The primary purpose of a QQ plot is to measure the skewness and kurtosis of the empirical data.
No comments yet.