Hazard rate and reliability function predictions for future observations

Estimating reliability and hazard rate functions for various types of distributions based on sample information is an interesting problem in the statistical literature. The common and the simplest approach to this problem is to estimate the unknown parameters for the underlying distribution of concern and replace these unknown parameters in reliability and hazard rate functions by their estimators. However, this may lead to inconsistent coverage probabilities for the estimated functions. This classical approach may even perform much worse if one is interested in hazard rate and reliability function predictions for future observations. We will firstly introduce an efficient approximation algorithm for hazard rate and reliability functions, which achieves highly accurate coverage probabilities for their confidence intervals. We will also show that the convergence to asymptotic distributions for the functional estimators is quite fast. Secondly, we will discuss how predicted future order statistics of a specified distribution are obtained and utilized in this context. Results of a simulation study will also be shown for various types of location-scale distributions to demonstrate the efficiency of the proposed method for future observations.
Citation Formats
B. Sürücü, “Hazard rate and reliability function predictions for future observations,” presented at the 8th International Conference of the ERCIM WG on Computational and Methodological Statistics, 12 - 14 December 2015, 2015, Accessed: 00, 2021. [Online]. Available: http://cmstatistics.org/CMStatistics2015/docs/BoA%20CFE-CMStatistics%202015.pdf?20160122015943.