On the Fisher information in record data

The Fisher information contained in records, weak records and numbers of records are discussed in this paper. In the case when the initial distribution belongs to the exponential family, the Fisher information contained in record values as well as in record values and record times are found analytically. A new inverse sampling plan (ISP-II) is considered next and some results on Fisher information in record statistics obtained from ISP-II are then derived. We also finally propose some new estimators based on records and weak records.