A Simulation Study on Confidence Interval Procedures of Some Mean Cumulative Function Estimators

• Activity Number: 18
• Type: Topic Contributed
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Quality and Productivity Section
• Author(s): Huaiqing Wu*+ and Jianying Zuo and William Q. Meeker
• Companies: Iowa State University and Bank of America and Iowa State University
• Keywords: mean cumulative function ; MCF ; nonhomogeneous Poisson process ; nonparametric estimation ; recurrence data

Abstract

Recurrence data are collected to study the recurrent events on biological, physical, and other systems. Quantities of interest include the mean cumulative number of events and the mean cumulative cost of events. The mean cumulative function (MCF) can be estimated with nonparametric methods or by fitting parametric models, and many procedures have been suggested to construct confidence intervals (CIs) for the MCF. This talk presents the results of a large simulation study that was designed to compare five CI procedures for both nonparametric and parametric estimation. When doing parametric estimation, we assume the power law non-homogeneous Poisson process (NHPP) model. Our results include evaluation of these procedures when they are used for window-observation recurrence data where recurrence histories of some systems are available only in observation windows with gaps in between.