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.

Focuses on the development and assessment of confidence intervals for proportions Contains numerous easy-to-understand examples Includes a derivation of the exact probability mass function of the KaplanMeier productlimit estimator

Autorentext

Lawrence Leemis graduated with a PhD in Industrial Engineering from Purdue University, USA. He is currently a Professor in the Department of Mathematics at William & Mary, USA.

Heather Krehbiel graduated with a PhD in Statistics from Duke University, USA. She is currently a Professor in the Department of Mathematics at William & Mary, USA.

Yuxin Qin graduated with a BS in Mathematics and Art from William & Mary, USA. She is currently an actuary at Willis Towers Watson, USA.

Hayeon Park graduated with a BS in Mathematics and Economics from William & Mary, USA. She is currently an actuary at Travelers, USA.

Kexin Feng graduated with a BS in Mathematics and Economics from William & Mary, USA. She received her PhD in Economics from the California Institute of Technology.
She is currently a Postdoctoral Associate at the Yale Economic Growth Center.

Xingyu Wang graduated with a BS in Mathematics and Economics from William & Mary, USA. She is currently a PhD student in Statistics at the University of Washington, USA.

Inhalt

Confidence Intervals.- Confidence Intervals for Proportions.- Optimal Confidence Intervals for Proportions.- KaplanMeier ProductLimit Estimator.- Probability Distribution of the KaplanMeier Estimator.- Bias in the KaplanMeier Estimator.- Survival Confidence Interval Coverage.