Reconstructing past fractional record values

In this paper, reconstructing past fractional upper (lower) records from any absolutely continuous distribution is proposed. For this purpose, two pivotal quantities are given and their exact distributions are derived. More detailed results, including the case of unknown parameters, are given for the exponential and Fre´chet distributions. Moreover, the exact mean square reconstructor errors are obtained and some comparisons between the pivotal quantities are performed. To explore the efficiency of the obtained results, a simulation study is conducted and two real data sets are analyzed.