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IAI Actuarial Core Principles · Actuarial Statistics · Hypothesis testing and goodness of fit

A Kolmogorov-Smirnov test compares an empirical distribution function with a fully specified continuous distribution. Which statement about the test statistic is correct?

The Kolmogorov-Smirnov statistic is the maximum absolute vertical distance between the empirical distribution function and the hypothesised distribution function. It is not a frequency-based chi-square sum, a rank sum or a sign count.

  1. AIt is the largest absolute vertical difference between the empirical and hypothesised distribution functionsCorrect
  2. BIt is the sum of squared differences between observed and expected frequencies
  3. CIt is the sum of the ranks of the smaller sample
  4. DIt is the number of positive differences among paired observations
  5. It is the average absolute difference between the two distribution functions

Explanation

The KS statistic is D = max over x of |F_n(x) − F0(x)|, the supremum vertical gap. The sum of squared frequency differences belongs to chi-square, rank sums to Mann-Whitney, and the count of positive signs to the sign test.

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