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IAI Actuarial Core Principles · Actuarial Statistics · Exploratory data analysis

A normal Q-Q plot of residuals from a claims model shows points that follow the reference line in the middle but curve sharply upwards at the right end and sharply downwards at the left end. The most appropriate conclusion is that the residuals:

The residuals have heavier tails than the normal distribution. Sample quantiles are more extreme than theoretical normal quantiles at both ends, giving an S-shaped Q-Q plot, which indicates excess kurtosis rather than skewness.

  1. Aare right-skewed
  2. Bare left-skewed
  3. Chave lighter tails than the normal distribution
  4. Dhave heavier tails than the normal distributionCorrect
  5. are normally distributed

Explanation

When sample quantiles are more extreme than normal quantiles at both ends (high at right, low at left), the data have more mass in the tails, meaning heavier tails. Skewness would show a one-sided curve in the same direction at both ends.

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