For counts {n i }, the power divergence statistic for testing goodness of fit is for-0

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For counts {n_i}, the power divergence statistic for testing goodness of fit is

for-0<λ<o. Χ7 Σ

a. For Î» = 1, show that this equals X².

b. As Î» †’ 0, show that it converges to G².

c. As Î»†’ €“1, show that it converges to 2ˆ‘µÌ‚_i log (µÌ‚_i/n_i), the minimum discrimination information statistic (Gokhale and Kuliback 1978).

d. For Î» = €“1/2 show that it equals 4 ˆ‘(ˆšn_i €“ ˆšµÌ‚_i)², the Freeman€“TukLy statistic (Freeman and Tukey 1950).

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Categorical Data Analysis

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For counts {n i }, the power divergence statistic for testing goodness of fit is for-0

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for-0<λ

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a n i n i i i n i i i n i i i X 2 n i i X 2 bc Use fact ...View the full answer

Categorical Data Analysis

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