Let X1,..., Xn be iid negative binomial(r, p). We want to construct some approximate confidence intervals for

Question:

Let X1,..., Xn be iid negative binomial(r, p). We want to construct some approximate confidence intervals for the negative binomial parameters.
(a) Calculate Wilks' approximation (10.4.3) and show how to form confidence intervals with this expression.
(b) Find an approximate 1 - α confidence interval for the mean of the negative binomial distribution. Show how to incorporate the continuity correction into your interval.
(c) The aphid data of Exercise 9.23 can also be modeled using the negative binomial distribution. Construct an approximate 90% confidence interval for the aphid data using the results of part (b). Compare the interval to the Poisson-based intervals of Exercise 9.23.