Separate expressions for method of moments

Reference no: EM131002610

Given a random sample, X1 , X2 ,.. ., Xn from a negative binomial NBi(k, p) population, (i) Obtain a method of moments estimate of θ1 = k and θ2 = p explicitly in terms of the ?rst two moments, M1 and M2.

(ii) If k is speci?ed (as it is in many cases), obtain two separate expressions for method of moments estimate for p based on M1 and M2 .

(iii) When k is speci?ed, obtain a maximum likelihood estimate (MLE) for p and compare it with the method of moments estimate obtained in (ii).

Reference no: EM131002610

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