That would be expected if the positive and negative

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Unformatted text preview: elations Test 4 Methods of graduation Preliminaries Graduation by Parametric Formula Graduation by Reference to a Standard Table Graphical graduation Statistical Tests The Effect of Duplicate policies 40/72 Actuarial Statistics – Module 8: Method of Graduation Statistical tests Grouping of Signs Test Grouping of Signs test (Stevens’ test) I Purpose Test for overgraduation Test groups of deviations of the same sign (runs) Compare the number of groups (runs) of deviations of the same sign with the no. that would be expected if the positive and negative signs were arranged in random order. (Fewer runs than expected if overgraduated) Assume that of the m deviations there are n1 positive and n2 negative Null hypothesis: the given n1 positive deviations and n2 negative deviations are in random order Test Statistic 40/72 G = Number of groups of positive zx ’s Actuarial Statistics – Module 8: Method of Graduation Statistical tests Grouping of Signs Test Grouping of Signs test (Stevens’ test) II compute probability of G groups given n1 and n2 +1 there are n2t ways to arrange t positive groups among the n2 negative deviations − there are nt1−11 ways to arrange n1 positive deviations into t groups m there are n1 ways to arrange n1 positive and n2 negative deviations probability of exactly t positive groups (hypergeometric distribution) n1 −1 t −1 n2 +1 t m n1 41/72 Actuarial Statistics – Module 8: Method of Graduation Statistical tests Grouping of Signs Test Grouping of Signs test (Stevens’ test) III use one-tailed test by finding the smallest k such that t =k Pr (G ≤ k ) = t =1 n1 −1 t −1 n2 +1 t m n1 ≥ 0.05 which implies Pr (G ≤ l ) < 0.05 for any l < k . The critical value of the test can be found on Page 189 of the Tables if G ≤ k , we reject the null hypothesis, ie, that the rates are overgraduated (the rates do not adhere closely enough to the crude data and may be consistently too high or too low over certain parts of the table) 42/72 Actuarial Statistics – Module...
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This document was uploaded on 04/03/2014.

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