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

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

for-0<λ<o. Χ7 Σ


a. For λ = 1, show that this equals X2.

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

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

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

for-0

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