Editing Zipf's law (section)

==Empirical testing==

Empirically, a data set can be tested to see whether Zipf's law applies by checking the [[goodness of fit]] of an empirical distribution to the hypothesized power law distribution with a [[Kolmogorov–Smirnov test]], and then comparing the (log) likelihood ratio of the power law distribution to alternative distributions like an exponential distribution or lognormal distribution.<ref name=Clausetetal2009>{{cite journal |last1=Clauset |first1=A. |last2=Shalizi |first2=C.R. |last3=Newman |first3=M.E.J. |year=2009 |title=Power-law distributions in empirical data |journal=[[SIAM Review]] |volume=51 |issue=4 |pages=661–703 |doi=10.1137/070710111 |arxiv=0706.1062 |bibcode=2009SIAMR..51..661C }}</ref>

Zipf's law can be visualized by [[graph of a function|plotting]] the item frequency data on a [[log-log]] graph, with the axes being the [[logarithm]] of rank order, and logarithm of frequency. The data conform to Zipf's law with exponent {{mvar|s}} to the extent that the plot approximates a [[linear equation|linear]] (more precisely, [[affine function|affine]]) function with slope {{mvar|−s}}. For exponent {{nobr|{{math| ''s'' {{=}} 1 }} ,}} one can also plot the reciprocal of the frequency (mean interword interval) against rank, or the reciprocal of rank against frequency, and compare the result with the line through the origin with slope {{math| 1&nbsp;.}}<ref name=Powers1998/>