零膨胀泊松分布参数的固定宽度置信区间构造方法
Construction of Fixed-Width Confidence Intervals for Zero-Inflated Poisson Distributions Parameters
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摘要: 评估置信区间的两个常用准则为区间宽度与覆盖率,研究同时达到给定的区间长度与名义覆盖率的区间估计在实际应用中有重要的价值,但这在固定样本量的情况下是无法实现的. 应用序贯方法和两阶段抽样方法,乃至多阶段抽样方法是解决这一问题的常用途径.本文对零膨胀泊松分布的两个参数, 取零概率p和泊松均值参数lambda,进行了固定宽度置信区间的序贯方法和两阶段方法的研究,证明了所提出的所有序贯过程与两阶段过程的渐近相合性与有效性,并通过蒙特卡罗模拟研究展示了所提出方法的效果,并考虑了不同情况下最优固定样本量随两个参数的变化趋势,并通过实证分析来说明方法的应用价值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 zero-inflated Poisson distribution with a probability mass p and Poisson mean parameter \lambda, the construction of fixed-width confidence intervals for (\lambda,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.