On the accuracy of approximation of the negative binomial distribution by the gamma distribution and convergence rate of the distributions of some statistics to the Student distribution (Q493858)

The main result here is a non-uniform bound on the difference between the distribution functions of a negative binomial and a gamma random variable. The authors go on to consider the case of asymptotically normally distributed statistics, based on a sample whose size has a negative binomial distribution. Explicit rates of convergence of such statistics to Student's \(t\)-distribution are given.