Comparing the Fisher information in record data and random observations

Abstract

We compare the Fisher information (FI) contained in the firstn record values and record times with the FI inn i. i. d. observations. General results are established for exponential family and Weibull type setups, and a summary table is provided listing several common distributions. We show that the FI in record data improves notably once the record times are included, often changing from being less to being equal or greater than the FI in a random sample of the same size. The behavior in the Weibull case is surprising. There it depends onn, whether the record or the i.i. d. observations have more FI. We propose new estimators based on record data. The results may be of interest in some life testing situations.