Fisher information in k-records

We derive some general results on the Fisher information (FI) contained in the upper (or lower) k-record values and associated k-record times generated from an i.i.d. sample of fixed size from a continuous distribution. We apply the results to obtain the FI in both upper and lower k-record data from an exponential distribution. We propose two estimators of the exponential mean, based on the upper and lower k-record data, and discuss their small sample properties. We also consider k-record data from an inverse sampling plan, and present general formulas for the FI contained in it.