Erqian Li, Maozai Tian

【Abstract】

Interval width and coverage probability are two criteria for evaluating confidence intervals. It’s quite worthwhile to investigate fixed-width confidence intervals with a prescribed nominal level, which, in generally speaking, is hardly realized in fixed-sample-size circumstances. A common way to deal with this problem is to apply sequential methods and two-stage sampling or even multi-stage sampling. For zeroinflated Poisson distribution with a probability mass p and Poisson mean parameter A, the construction of fixed-width confidence intervals for(A, p)is conducted in this paper, including sequential and two-stage procedures. Each procedure is demonstrated to satisfy asymptotic consistency and efficiency. The variation of optimal fixed-sample size by the two parameters is considered under different situations and simulation performance is displayed by Monte Carlo simulation. A real data analysis is also implemented for application.

【Keywords】

fixed-width confidence interval, sequential procedures, two-stage sampling, zero-inflated poisson distribution