https://wiki.lojban.io/index.php?action=history&feed=atom&title=cnanlime cnanlime - Revision history 2026-05-07T10:13:12Z Revision history for this page on the wiki MediaWiki 1.45.3 https://wiki.lojban.io/index.php?title=cnanlime&diff=3128&oldid=prev Nalvaizmiku: Import words via API 2026-01-13T14:37:35Z <p>Import words via API</p> <p><b>New page</b></p><div>==== valsi ====<br /> cnanlime<br /> ==== type ====<br /> fu&#039;ivla<br /> ==== creator ====<br /> [[personal/krtisfranks|krtisfranks]]<br /> ==== time entered ====<br /> Sun Apr 1 01:14:50 2018<br />  <br /> == English ==<br /> === Definition #70580 - Preferred ===<br />  <br /> ==== definition ====<br /> x&lt;sub&gt;1&lt;/sub&gt; is the generalized weighted Lehmer mean of data x&lt;sub&gt;2&lt;/sub&gt; (completely specified ordered multiset/list of numbers) of Lehmer order x&lt;sub&gt;3&lt;/sub&gt; (either a single extended-real number xor an ordered pair of two extended-real numbers) with weights x&lt;sub&gt;4&lt;/sub&gt; (completely specified ordered multiset/list of numbers with the same cardinality as x&lt;sub&gt;2&lt;/sub&gt;; defaults according to the Notes).<br /> ==== notes ====<br /> <br /> Possibly dimensionful. If the cardinality of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; is &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;n&lt;/i&gt;&lt;/span&gt;, then the cardinality of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;4&lt;/sub&gt;&lt;/span&gt; is also &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;n&lt;/i&gt;&lt;/span&gt; and, moreover, the weights default to &lt;span class=&quot;MATH&quot;&gt;1/&lt;i&gt;n&lt;/i&gt;&lt;/span&gt; each. If &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt;&lt;/span&gt; is a single extended-real number &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;p&lt;/i&gt;&lt;/span&gt;, then MATH<br /> $x_3 = (p, p-1)$<br /> <br /> &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt; = (&lt;i&gt;p&lt;/i&gt;, &lt;i&gt;p&lt;/i&gt; - 1)&lt;/span&gt; also. If MATH<br /> $x_3 = (p, q)$<br /> <br /> &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt; = (&lt;i&gt;p&lt;/i&gt;, &lt;i&gt;q&lt;/i&gt;)&lt;/span&gt; validly for real &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;p&lt;/i&gt;&lt;/span&gt;&amp;&lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;q&lt;/i&gt;&lt;/span&gt;, then &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt; =&lt;/span&gt;Sum MATH<br /> $(w_i y_i^p, i$<br /> <br /> &lt;span class=&quot;MATH&quot;&gt;(&lt;i&gt;w&lt;/i&gt;&lt;sub&gt;i&lt;/sub&gt;&lt;i&gt;y&lt;/i&gt;&lt;sub&gt;i&lt;/sub&gt;&lt;sup&gt;p&lt;/sup&gt;, &lt;i&gt;i&lt;/i&gt;&lt;/span&gt; in Set MATH<br /> $(1,...,n))/$<br /> <br /> &lt;span class=&quot;MATH&quot;&gt;(1,..., &lt;i&gt;n&lt;/i&gt;))/&lt;/span&gt;Sum MATH<br /> $(w_i y_i^q, i$<br /> <br /> &lt;span class=&quot;MATH&quot;&gt;(&lt;i&gt;w&lt;/i&gt;&lt;sub&gt;i&lt;/sub&gt;&lt;i&gt;y&lt;/i&gt;&lt;sub&gt;i&lt;/sub&gt;&lt;sup&gt;q&lt;/sup&gt;, &lt;i&gt;i&lt;/i&gt;&lt;/span&gt; in Set MATH<br /> $(1,...,n))$<br /> <br /> &lt;span class=&quot;MATH&quot;&gt;(1,..., &lt;i&gt;n&lt;/i&gt;))&lt;/span&gt;, where &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;y&lt;/i&gt;&lt;sub&gt;i&lt;/sub&gt;&lt;/span&gt; is the &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;i&lt;/i&gt;&lt;/span&gt;th term of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; for all &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;i&lt;/i&gt;&lt;/span&gt;, &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;w&lt;/i&gt;&lt;sub&gt;i&lt;/sub&gt;&lt;/span&gt; is the &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;i&lt;/i&gt;&lt;/span&gt;th term of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;4&lt;/sub&gt;&lt;/span&gt; for all &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;i&lt;/i&gt;&lt;/span&gt;, and &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;n&lt;/i&gt;&lt;/span&gt; is the cardinality of &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt; (and thus &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;4&lt;/sub&gt;&lt;/span&gt;). If &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt;&lt;/span&gt; equals positive infinity ([[ma&#039;uci&#039;i|ma&#039;uci&#039;i]]), then the result &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; is the maximum of the data &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt;; if &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;3&lt;/sub&gt;&lt;/span&gt; equals negative infinity ([[ni&#039;uci&#039;i|ni&#039;uci&#039;i]]), then the result &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;1&lt;/sub&gt;&lt;/span&gt; is the minimum of the data &lt;span class=&quot;MATH&quot;&gt;&lt;i&gt;x&lt;/i&gt;&lt;sub&gt;2&lt;/sub&gt;&lt;/span&gt;.<br /> <br /> ==== gloss words ====<br /> <br /> &lt;ul&gt;&lt;li&gt;[[natlang/en/contraharmonic mean|contraharmonic mean]]&lt;/li&gt;&lt;li&gt;[[natlang/en/Lehmer average|Lehmer average]]&lt;/li&gt;&lt;li&gt;[[natlang/en/Lehmer mean|Lehmer mean]]&lt;/li&gt;&lt;/ul&gt;<br /> <br /> ==== created by ====<br /> [[personal/krtisfranks|krtisfranks]]<br /> ==== vote information ====<br /> 1<br /> <br /> ==== time ====<br /> Sun Apr 1 02:44:44 2018<br /> <br /> <br /> <br /> &lt;br/&gt;&lt;font size=&quot;+1&quot;&gt;Examples&lt;/font&gt;<br /> &lt;hr/&gt;<br /> &lt;dl&gt;<br /> &lt;/dl&gt;<br /> <br /> === Etymology ===</div> Nalvaizmiku