https://en.formulasearchengine.com/index.php?action=history&feed=atom&title=Schatten_class_operator 2026-04-17T02:52:28Z Revision history for this page on the wiki MediaWiki 1.43.0-wmf.28 https://en.formulasearchengine.com/index.php?title=Schatten_class_operator&diff=16867&oldid=prev 2013-03-16T22:51:55Z

<p><a href="/index.php?title=User:Addbot&amp;action=edit&amp;redlink=1" class="new" title="User:Addbot (page does not exist)">Bot:</a> Migrating 1 interwiki links, now provided by <a href="https://en.wikipedia.org/wiki/Wikidata" class="extiw" title="wikipedia:Wikidata">Wikidata</a> on <a href="/index.php?title=D:q2231600&amp;action=edit&amp;redlink=1" class="new" title="D:q2231600 (page does not exist)">d:q2231600</a></p> <table style="background-color: #fff; color: #202122;" data-mw="interface"> <col class="diff-marker" /> <col class="diff-content" /> <col class="diff-marker" /> <col class="diff-content" /> <tr class="diff-title" lang="en"> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td> <td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 00:51, 17 March 2013</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;">Andrew Simcox is the name his mothers </del>and <del style="font-weight: bold; text-decoration: none;">fathers gave him and he completely loves this name. I</del>'<del style="font-weight: bold; text-decoration: none;">ve usually cherished living in Kentucky but now I</del>'<del style="font-weight: bold; text-decoration: none;">m contemplating other options</del>. <del style="font-weight: bold; text-decoration: none;">One </del>of <del style="font-weight: bold; text-decoration: none;">the issues she loves most </del>is <del style="font-weight: bold; text-decoration: none;">canoeing and she's been performing </del>it for <del style="font-weight: bold; text-decoration: none;"> free psychic readings </del>([<del style="font-weight: bold; text-decoration: none;">http://www</del>.<del style="font-weight: bold; text-decoration: none;">zavodpm</del>.<del style="font-weight: bold; text-decoration: none;">ru</del>/<del style="font-weight: bold; text-decoration: none;">blogs/glennmusserrvji/14565-great-hobby-advice-assist-allow-you-get-going zavodpm</del>.<del style="font-weight: bold; text-decoration: none;">ru</del>]) <del style="font-weight: bold; text-decoration: none;">quite a whilst</del>. <del style="font-weight: bold; text-decoration: none;">He </del>is an <del style="font-weight: bold; text-decoration: none;">purchase clerk and it's some thing he truly enjoy</del>.&lt;<del style="font-weight: bold; text-decoration: none;">br&gt;&lt;br</del>&gt;<del style="font-weight: bold; text-decoration: none;">Feel free to visit my weblog: free </del>[<del style="font-weight: bold; text-decoration: none;">http://www.010-5260-5333.com/index.php?document_srl</del>=<del style="font-weight: bold; text-decoration: none;">1880&amp;mid</del>=<del style="font-weight: bold; text-decoration: none;">board_ALMP66 authentic psychic readings] - [http://www</del>.<del style="font-weight: bold; text-decoration: none;">weddingwall.com.au</del>/<del style="font-weight: bold; text-decoration: none;">groups</del>/<del style="font-weight: bold; text-decoration: none;">easy-advice-</del>for<del style="font-weight: bold; text-decoration: none;">-successful-personal-development-today/ http</del>:/<del style="font-weight: bold; text-decoration: none;">/www</del>.<del style="font-weight: bold; text-decoration: none;">weddingwall.com.au</del>/<del style="font-weight: bold; text-decoration: none;">groups/easy</del>-<del style="font-weight: bold; text-decoration: none;">advice-for-successful-personal-development-today/</del>]<del style="font-weight: bold; text-decoration: none;">,</del></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">In [[statistics]] </ins>and <ins style="font-weight: bold; text-decoration: none;">[[computer software]],  a '''convolution random number generator'</ins>'' <ins style="font-weight: bold; text-decoration: none;">is a [[pseudo-random number sampling]] method that can be used to generate [[random variate]]s from certain classes of [[probability distribution]]</ins>. <ins style="font-weight: bold; text-decoration: none;">The particular advantage of this type </ins>of <ins style="font-weight: bold; text-decoration: none;">approach </ins>is <ins style="font-weight: bold; text-decoration: none;">that </ins>it <ins style="font-weight: bold; text-decoration: none;">allows advantage to be taken of existing software </ins>for <ins style="font-weight: bold; text-decoration: none;">generating random variates from other, usually non-uniform, distributions. However, faster algorithms may be obtainable for the same distributions by other more complicated approaches.</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">A number of distributions can be expressed in terms of the </ins>(<ins style="font-weight: bold; text-decoration: none;">possibly weighted) sum of two or more [</ins>[<ins style="font-weight: bold; text-decoration: none;">random variable]]s from other distributions</ins>. <ins style="font-weight: bold; text-decoration: none;">(The distribution of the sum is the [[convolution]] of the distributions of the individual random variables)</ins>.</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">== Example ==</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Consider the problem of generating a random variable with an [[Erlang distribution]], &lt;math&gt;X\ \sim \operatorname{Erlang}(k, \theta)&lt;</ins>/<ins style="font-weight: bold; text-decoration: none;">math&gt;</ins>. <ins style="font-weight: bold; text-decoration: none;">Such a random variable can be defined as the sum of ''k'' random variables each with an [[exponential distribution</ins>]<ins style="font-weight: bold; text-decoration: none;">] &lt;math&gt;\operatorname{Exp}(k \theta</ins>) <ins style="font-weight: bold; text-decoration: none;">\,&lt;/math&gt;</ins>. <ins style="font-weight: bold; text-decoration: none;">This problem </ins>is <ins style="font-weight: bold; text-decoration: none;">equivalent to generating a random number for a special case of the [[Gamma distribution]], in which the [[shape parameter]] takes </ins>an <ins style="font-weight: bold; text-decoration: none;">integer value</ins>.</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">Notice that:</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">:</ins>&lt;<ins style="font-weight: bold; text-decoration: none;">math</ins>&gt;<ins style="font-weight: bold; text-decoration: none;">\operatorname{E}</ins>[<ins style="font-weight: bold; text-decoration: none;">X] </ins>= <ins style="font-weight: bold; text-decoration: none;">\frac{1}{k \theta} + \frac{1}{k \theta} + \cdots + \frac{1}{k \theta} </ins>= <ins style="font-weight: bold; text-decoration: none;">\frac{1}{\theta} </ins>.<ins style="font-weight: bold; text-decoration: none;">&lt;</ins>/<ins style="font-weight: bold; text-decoration: none;">math&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">One can now generate &lt;math&gt;\operatorname{Erlang}(k, \theta)&lt;</ins>/<ins style="font-weight: bold; text-decoration: none;">math&gt; samples using a random number generator </ins>for <ins style="font-weight: bold; text-decoration: none;">the exponential distribution</ins>:</div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">if &lt;math&gt;X_i\ \sim \operatorname{Exp}(k \theta)&lt;</ins>/<ins style="font-weight: bold; text-decoration: none;">math&gt;&amp;nbsp; &amp;nbsp; then &lt;math&gt;X=\sum_{i=1}^k X_i \sim \operatorname{Erlang}(k,\theta) </ins>.<ins style="font-weight: bold; text-decoration: none;">&lt;</ins>/<ins style="font-weight: bold; text-decoration: none;">math&gt;</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div> </div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">{{unreferenced|date=November 2010}}</ins></div></td></tr> <tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">[[Category:Non</ins>-<ins style="font-weight: bold; text-decoration: none;">uniform random numbers]</ins>]</div></td></tr> </table>

en>Addbot https://en.formulasearchengine.com/index.php?title=Schatten_class_operator&diff=253909&oldid=prev 2010-03-07T13:38:50Z

<p>robot Adding: <a href="/index.php?title=De:Schatten-Klasse&amp;action=edit&amp;redlink=1" class="new" title="De:Schatten-Klasse (page does not exist)">de:Schatten-Klasse</a></p> <p><b>New page</b></p><div>Andrew Simcox is the name his mothers and fathers gave him and he completely loves this name. I&#039;ve usually cherished living in Kentucky but now I&#039;m contemplating other options. One of the issues she loves most is canoeing and she&#039;s been performing it for free psychic readings ([http://www.zavodpm.ru/blogs/glennmusserrvji/14565-great-hobby-advice-assist-allow-you-get-going zavodpm.ru]) quite a whilst. He is an purchase clerk and it&#039;s some thing he truly enjoy.&lt;br&gt;&lt;br&gt;Feel free to visit my weblog: free [http://www.010-5260-5333.com/index.php?document_srl=1880&amp;mid=board_ALMP66 authentic psychic readings] - [http://www.weddingwall.com.au/groups/easy-advice-for-successful-personal-development-today/ http://www.weddingwall.com.au/groups/easy-advice-for-successful-personal-development-today/],</div>

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