  We consider the well known \emph{Least Recently Used} (LRU) replacement
algorithm and analyze it under the independent reference model and generalized
power-law demand. For this extensive family of demand distributions we derive a
closed-form expression for the per object steady-state hit ratio. To the best
of our knowledge, this is the first analytic derivation of the per object hit
ratio of LRU that can be obtained in constant time without requiring laborious
numeric computations or simulation. Since most applications of replacement
algorithms include (at least) some scenarios under i.i.d. requests, our method
has substantial practical value, especially when having to analyze multiple
caches, where existing numeric methods and simulation become too time
consuming.
