  We study statistics of records in a sequence of random variables. These
identical and independently distributed variables are drawn from the parent
distribution rho. The running record equals the maximum of all elements in the
sequence up to a given point. We define a superior sequence as one where all
running records are above the average record, expected for the parent
distribution rho. We find that the fraction of superior sequences S_N decays
algebraically with sequence length N, S_N ~ N^{-beta} in the limit N-->infty.
Interestingly, the decay exponent beta is nontrivial, being the root of an
integral equation. For example, when rho is a uniform distribution with compact
support, we find beta=0.450265. In general, the tail of the parent distribution
governs the exponent beta. We also consider the dual problem of inferior
sequences, where all records are below average, and find that the fraction of
inferior sequences I_N decays algebraically, albeit with a different decay
exponent, I_N ~ N^{-alpha}. We use the above statistical measures to analyze
earthquake data.
