what kind of probability distribution can be used to model numeral-noun combinations? - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T10:59:09Z http://mathoverflow.net/feeds/question/23991 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/23991/what-kind-of-probability-distribution-can-be-used-to-model-numeral-noun-combinati what kind of probability distribution can be used to model numeral-noun combinations? danatel 2010-05-09T06:00:39Z 2010-05-09T15:12:57Z <p>I'am learning German (any other language will do). </p> <p>I choose randomly a countable noun - for example the noun "Hotel".</p> <p>I write the noun into google together with German numeral for "two" in double quotes: "zwei Hotels" and write down the number of matches (229000).</p> <p>I repeat the experiment with 3 - "drei Hotels" (14100 matches), 4 (8490), 5 (3670), 6 (3160), 7 (3700) ...</p> <p>What probability distribution should I expect to obtain?</p> http://mathoverflow.net/questions/23991/what-kind-of-probability-distribution-can-be-used-to-model-numeral-noun-combinati/24016#24016 Answer by Martin M. W. for what kind of probability distribution can be used to model numeral-noun combinations? Martin M. W. 2010-05-09T13:13:48Z 2010-05-09T15:12:57Z <p>The distribution probably depends on the kind of noun, although Benford's law might cover a lot of cases.</p> <p>There's some related empirical data from, of all places, the art world! Artist Golan Levin created a project based on the volume of search results for the numbers one through a million. There are a lot of interesting outliers, of course: 1040, 90210, recent years. But one thing that leaps out is that there are spikes at round numbers (multiples of 100, 10, 5, and so on). I'd be interested to know if there are models of these "round number" peaks.</p> <p>You can see the project here, which charts all million data points: <a href="http://www.turbulence.org/Works/nums/" rel="nofollow">http://www.turbulence.org/Works/nums/</a></p> <p>And here are two graphs from the piece, of the frequencies of the first few hundreds of numbers:</p> <p><img src="http://i.imgur.com/xmrh5.png" alt="alt text"></p> <p>and thousands (the vertical scale is a bit cut off):</p> <p><img src="http://i.imgur.com/s6dgL.png" alt="alt text"></p>