Bayesian Estimation and Prediction for the Power Law Process with Left-Truncated Data
| Autor: | Man-Lai Tang, Guo-Liang Tian, Jun-Wu Yu |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
0301 basic medicine
Bayes estimator Computer science Bayesian probability Prediction interval computer.software_genre Power law 03 medical and health sciences 030104 developmental biology 0302 clinical medicine 030220 oncology & carcinogenesis Credible interval Point (geometry) Data mining Point estimation computer Algorithm Reliability (statistics) |
| Zdroj: | Journal of Data Science. 9:445-470 |
| ISSN: | 1683-8602 1680-743X |
| DOI: | 10.6339/jds.201107_09(3).0009 |
| Popis: | The power law process (PLP) (i.e., the nonhomogeneous Poisson process with power intensity law) is perhaps the most widely used model for analyzing failure data from reliability growth studies. Statistical infer- ences and prediction analyses for the PLP with left-truncated data with classical methods were extensively studied by Yu et al. (2008) recently. However, the topics discussed in Yu et al. (2008) only included maximum likelihood estimates and condence intervals for parameters of interest, hy- pothesis testing and goodness-of-t test. In addition, the prediction limits of future failure times for failure-truncated case were also discussed. In this paper, with Bayesian method we consider seven totally dierent prediciton issues besides point estimates and prediction limits for xn+k. Specically, we develop estimation and prediction methods for the PLP in the presence of left-truncated data by using the Bayesian method. Bayesian point and credible interval estimates for the parameters of interest are derived. We show how ve single-sample and three two-sample issues are addressed by the proposed Bayesian method. Two real examples from an engine develop- ment program and a repairable system are used to illustrate the proposed methodologies. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|