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IAI Actuarial Core Principles · Actuarial Statistics · Exploratory data analysis

An actuary draws a normal Q-Q plot of 200 standardised residuals, with theoretical quantiles on the horizontal axis and sample quantiles on the vertical axis. The points follow the line in the centre, but at the right end they curve well above the line and at the left end well below it. What does this indicate?

The distribution has heavier tails than the normal. When the largest sample quantiles lie above the line and the smallest lie below it, the data produce more extreme values in both directions than a normal distribution would, which is characteristic of heavy tails.

  1. AThe distribution is negatively skewed
  2. BThe distribution has lighter tails than the normal
  3. CThe distribution has heavier tails than the normalCorrect
  4. DThe distribution is positively skewed with light tails
  5. The data are exactly normal with a different mean

Explanation

Extreme sample quantiles are more extreme than normal ones at both ends: upper above the line, lower below. That is the signature of heavy tails. Skewness would show a curve bending the same way at both ends. A different mean or variance only shifts or tilts the line.

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