The Analysis of Alternative Interval-Censored and Complete Data

Abstract

The paper considers an imputation algorithm of iterative single point quantiles for the analysis of the alternative interval-censored and complete data which is a new type of censoring data. The imputed virtual interval-censored data and right censored data are all given by a modified quantile imputation algorithm for general distributions, which is proposed in the paper for this new type censoring data. The simulation results indicate that the proposed modified quantile imputation algorithm seems to be applicable and stable for the estimation of parameters with all distributions. The case of Weibull distribution that has not a closed form for parameter estimations has been studied in details by using the proposed algorithm. Specially, for exponential distribution, we proved that the convergence of the algorithm holds under general conditions, which is an extension of the previous work. The work done in the paper can be used to solve the problems of parameter estimation even in those cases when it is impossible to obtain a complete sample under some complex circumstances. This may bring a new way to balance higher estimation precision and cost on data collections in practice.

Key Words:

• Convergence
• imputation algorithm
• interval-censored and complete data
• simulation
• upper bound
• reliability.

Additional information

Notes on contributors

Dejing Kong

Dejing Kong received his B. S. degree of statistics from Shandong University, China, in 2012, and is working towards the Ph.D. degree in Management Science and Engineering at the School of Management and Economics, Beijing Institute of Technology, Beijing, China. His research interests are statistical inference and modeling, system reliability and simulation.

Lirong Cui

Lirong Cui is a Professor in the School of Management & Economics at Beijing Institute of Technology, China. He received his Ph.D. degree in Probability and Statistics from the University of Wales, UK in 1994. He has worked on quality and reliability related problems since 1986, and published more than 100 papers and technical reports. In 2000, he co-authored of a book on reliability which was published by Kluwer Academic Publishers. Now he is the only person from mainland China to serve as an associate editor of IEEE Transactions on Reliability, he also serves as an associate editor of Communications in Statistics: Theory and Methods, Simulation and Computation. In 2005, He was awarded the new century excellent talents in university of China. His recent research interests are stochastic modeling, quality and reliability engineering, simulation and optimization, operations research, applications of probability and statistics in various fields.

Xibin Zhao

Xibin Zhao is an Associate Professor at the School of Software, Tsinghua University, China. He received his Ph.D. in 2004 from the School of Computer Science and Telecommunication Engineering, Jiangsu University, China. His research interests include distributed system control, and system safety management.