Confidence Intervals for Proportions

This innovative book explores methodologies for constructing confidence intervals for proportions. It compares existing techniques and introduces new procedures developed by the authors, emphasizing the actual coverage function to assess their effectiveness. It covers various applications, such as estimating success rates in Monte Carlo simulations, gauging electoral support, assessing project completion rates, and evaluating product reliability. It provides analysts with both point and interval estimators, highlighting how interval estimators offer precision for point estimates. Key focus is placed on selecting appropriate confidence interval procedures and understanding their statistical properties. While traditional methods offer only approximate intervals, this work examines popular options and derives their statistical characteristics, providing guidelines for practitioners. Additionally, it discusses pointwise confidence intervals for survivor functions from randomly right-censored datasets, appealing to reliability engineers and survival analysts. It includes practical applications through functions in R, allowing practitioners to compute confidence intervals and visualize their coverage. As the first of its kind to focus solely on this topic, the book serves as a valuable resource for advanced students and can support a one-semester course on confidence intervals for proportions, making a significant contribution to the field of statistics.