Characterization of hazard function factorization by Fisher information in minima and upper record values

The hazard function is an important characteristic for the analysis of reliability data. It is therefore of interest to see under what conditions it can be expressed as the product of a function of the variable and a function of the parameter. We show that such a factorization can be characterized by the property of Fisher information in minima and upper record values. We present similar results for the reversed hazard rate by the property of Fisher information in maxima and lower record values. These properties imply the characterization of two classes of exponential families.