Suppose (X; Y ) is distributed as one of the most famous bivariate dis- tributions, namely Gumbel s bivariate exponential distribution Type II (GBVE). We investigate some properties of the Fisher Information (FI) contained in the sequence of record values and their concomitants (f(Rn;R[n]); n ¸ 1g) about the unknown parameters of model. Three schemes are considered and in each scheme one of the parameters of GBVE distribution is assumed to be unknown the Fisher information about the unknown parameter contained in record values and their concomitants is investigated. The behavior of information measure with respect to n and other known parameters is studied. Also, we calculate and tabulate the relative e±ciency of the optimal estimator (i.e. the estimator with a variance equal to the Crame\\\\\\\\\\\\\\\'r Rao lower bound) of unknown parameter based on the ¯rst n records and their concomitants with respect to the desired estimator on the basis of a sample of size n of pairs (X; Y ) from the parent distribution.

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