Sensitivity Analysis of Multistage Sampling to Departure of an Underlying Distribution from Normality with Computer Simulations

• Published in: Sequential analysis Vol. 34; no. 4; pp. 532 - 558
• Main Authors: Hamdy, H. I., Son, M. S., Yousef, A. S.
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 02.10.2015; Taylor & Francis Ltd
• Subjects: Acceleration; Confidence intervals; Kurtosis; Monte Carlo simulation; Normal distribution; One-by-one sequential sampling; Operating characteristic curve; Sampling; Second-order approximations; Sensitivity analysis; Skewness; Triple sampling
• ISSN: 0747-4946; 1532-4176
• DOI: 10.1080/07474946.2015.1099951

The current study examines empirically the impact of using normal distribution-based theory and methodology of multistage sampling procedures when the population distribution moves away from normality. We focus on some relevant kinds of departures and illustrate the impact of such departures on the quality of multistage inference. We also address the quality of inference due to shifts in parameters and investigate the extent of sensitivity of both coverage probability and the type II error probability. We do so by examining the capabilities of a fixed-width confidence interval to detect possible shifts in the true parameters occurring outside the confidence interval. Extensive sets of Monte Carlo simulations are reported in a number of interesting situations to highlight small to moderate to large-sample-size performances due to change(s) in the underlying distribution or shifts in the population parameters.