sec self-organizing lists geometric probability distribution can yield quite different results example calculate the expected cost for searching list ordered by frequency when the probabilities are defined as / if < < pi / - if thencn ( / = for this examplethe expected number of accesses is constant this is because the probability for accessing the first record is highthe second is much lower but still much higher than for record threeand so on this shows that for some probability distributionsordering the list by frequency can yield an efficient search technique in many search applicationsreal access patterns follow rule of thumb called the / rule the / rule says that of the record accesses are to of the records the values of and are only estimatesevery application has its own values howeverbehavior of this nature occurs surprisingly often in practice (which explains the success of caching techniques widely used by disk drive and cpu manufacturers for speeding access to data stored in slower memorysee the discussion on buffer pools in section when the / rule applieswe can expect reasonable search performance from list ordered by frequency of access example the / rule is an example of zipf distribution naturally occurring distributions often follow zipf distribution examples include the observed frequency for the use of words in natural language such as englishand the size of the population for cities ( view the relative proportions for the populations as equivalent to the "frequency of use"zipf distributions are related to the harmonic series defined in equation define the zipf frequency for item in the distribution for records as /(ihn (see exercise the expected cost for the series whose members follow this zipf distribution will be cn = /ihn /hn nloge