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

Which statement about the Kolmogorov-Smirnov test for a fully specified continuous distribution is correct?

The Kolmogorov-Smirnov statistic is the maximum absolute gap between the empirical and hypothesised CDFs. For a fully specified continuous distribution its null distribution is the same whatever the hypothesised distribution, and no grouping into cells is needed.

  1. AIts statistic is the largest absolute difference between the empirical and hypothesised CDFs, and its null distribution does not depend on the hypothesised distributionCorrect
  2. BIt requires data to be grouped into cells with expected counts of at least 5
  3. CIts degrees of freedom equal the number of cells minus one
  4. DIt is most sensitive to differences in the extreme tails
  5. Its statistic is a sum of squared standardised differences over cells

Explanation

The KS statistic is the supremum of |Fn - F0|, and for continuous F0 with fully specified parameters its null distribution is distribution-free. Grouping and degrees of freedom belong to the chi-squared test. KS is usually more sensitive near the centre than the tails.

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