https://www.reliawiki.com/index.php?action=history&feed=atom&title=Template%3ACharacteristics_of_the_gumbel_distribution
Template:Characteristics of the gumbel distribution - Revision history
2026-04-05T10:12:39Z
Revision history for this page on the wiki
MediaWiki 1.44.0
https://www.reliawiki.com/index.php?title=Template:Characteristics_of_the_gumbel_distribution&diff=30409&oldid=prev
Lisa Hacker: Redirected page to The Gumbel/SEV Distribution
2012-08-08T07:43:41Z
<p>Redirected page to <a href="/index.php/The_Gumbel/SEV_Distribution" title="The Gumbel/SEV Distribution">The Gumbel/SEV Distribution</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 07:43, 8 August 2012</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;">==Characteristics of the Gumbel Distribution==</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;">#REDIRECT </ins>[[<ins style="font-weight: bold; text-decoration: none;">The_Gumbel</ins>/<ins style="font-weight: bold; text-decoration: none;">SEV_Distribution</ins>]]</div></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;">Some of the specific characteristics of the Gumbel distribution are the following:</del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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;">:* The shape of the Gumbel distribution is skewed to the left. The Gumbel <math>pdf</math> has no shape parameter. This means that the Gumbel <math>pdf</math> has only one shape, which does not change.</del></div></td><td colspan="2" class="diff-side-added"></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;">:* The Gumbel <math>pdf</math> has location parameter <math>\mu ,</math> which is equal to the mode <math>\tilde{T},</math> but it differs from median and mean. This is because the Gumbel distribution is not symmetrical about its <math>\mu </math> .</del></div></td><td colspan="2" class="diff-side-added"></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;">:* As <math>\mu </math> decreases, the <math>pdf</math> is shifted to the left.</del></div></td><td colspan="2" class="diff-side-added"></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;">:* As <math>\mu </math> increases, the <math>pdf</math> is shifted to the right.</del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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;">Image:WB.16 gumbel pdf.png|center|250px| ]] </del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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;">:* As <math>\sigma <</del>/<del style="font-weight: bold; text-decoration: none;">math> increases, the <math>pdf</math> spreads out and becomes shallower.</del></div></td><td colspan="2" class="diff-side-added"></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;">:* As <math>\sigma </math> decreases, the <math>pdf</math> becomes taller and narrower.</del></div></td><td colspan="2" class="diff-side-added"></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;">:* For <math>T=\pm \infty ,</math> <math>pdf=0.</math> For <math>T=\mu </math> , the <math>pdf</math> reaches its maximum point <math>\frac{1}{\sigma e}</math></del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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;">[[Image:WB.16 effect of sigma.png|center|250px| ]] </del></div></td><td colspan="2" class="diff-side-added"></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> </div></td><td colspan="2" class="diff-side-added"></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;">:* The points of inflection of the <math>pdf</math> graph are <math>T=\mu \pm \sigma \ln (\tfrac{3\pm \sqrt{5}}{2})</math> or <math>T\approx \mu \pm \sigma 0.96242</math> .</del></div></td><td colspan="2" class="diff-side-added"></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;">:* If times follow the Weibull distribution, then the logarithm of times follow a Gumbel distribution. If <math>{{t}_{i}}</math> follows a Weibull distribution with <math>\beta </math> and <math>\eta </math> , then the <math>Ln({{t}_{i}})</math> follows a Gumbel distribution with <math>\mu =\ln (\eta )</math> and <math>\sigma =\tfrac{1}{\beta }</math> [[Appendix: Weibull References|[32]</del>]]<del style="font-weight: bold; text-decoration: none;">.</del></div></td><td colspan="2" class="diff-side-added"></td></tr>
</table>
Lisa Hacker
https://www.reliawiki.com/index.php?title=Template:Characteristics_of_the_gumbel_distribution&diff=24884&oldid=prev
Nicolette Young: /* Characteristics of the Gumbel Distribution */
2012-04-25T21:59:30Z
<p><span class="autocomment">Characteristics of the Gumbel Distribution</span></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 21:59, 25 April 2012</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l7">Line 7:</td>
<td colspan="2" class="diff-lineno">Line 7:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* As <math>\mu </math> increases, the <math>pdf</math> is shifted to the right.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* As <math>\mu </math> increases, the <math>pdf</math> is shifted to the right.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></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>[[Image:WB.16 gumbel pdf.png|center|<del style="font-weight: bold; text-decoration: none;">400px</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>[[Image:WB.16 gumbel pdf.png|center|<ins style="font-weight: bold; text-decoration: none;">250px</ins>| ]] </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* As <math>\sigma </math> increases, the <math>pdf</math> spreads out and becomes shallower.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* As <math>\sigma </math> increases, the <math>pdf</math> spreads out and becomes shallower.</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l13">Line 13:</td>
<td colspan="2" class="diff-lineno">Line 13:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* For <math>T=\pm \infty ,</math> <math>pdf=0.</math> For <math>T=\mu </math> , the <math>pdf</math> reaches its maximum point <math>\frac{1}{\sigma e}</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* For <math>T=\pm \infty ,</math> <math>pdf=0.</math> For <math>T=\mu </math> , the <math>pdf</math> reaches its maximum point <math>\frac{1}{\sigma e}</math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></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>[[Image:WB.16 effect of sigma.png|center|<del style="font-weight: bold; text-decoration: none;">400px</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>[[Image:WB.16 effect of sigma.png|center|<ins style="font-weight: bold; text-decoration: none;">250px</ins>| ]] </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* The points of inflection of the <math>pdf</math> graph are <math>T=\mu \pm \sigma \ln (\tfrac{3\pm \sqrt{5}}{2})</math> or <math>T\approx \mu \pm \sigma 0.96242</math> .</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* The points of inflection of the <math>pdf</math> graph are <math>T=\mu \pm \sigma \ln (\tfrac{3\pm \sqrt{5}}{2})</math> or <math>T\approx \mu \pm \sigma 0.96242</math> .</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* If times follow the Weibull distribution, then the logarithm of times follow a Gumbel distribution. If <math>{{t}_{i}}</math> follows a Weibull distribution with <math>\beta </math> and <math>\eta </math> , then the <math>Ln({{t}_{i}})</math> follows a Gumbel distribution with <math>\mu =\ln (\eta )</math> and <math>\sigma =\tfrac{1}{\beta }</math> [[Appendix: Weibull References|[32]]].</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* If times follow the Weibull distribution, then the logarithm of times follow a Gumbel distribution. If <math>{{t}_{i}}</math> follows a Weibull distribution with <math>\beta </math> and <math>\eta </math> , then the <math>Ln({{t}_{i}})</math> follows a Gumbel distribution with <math>\mu =\ln (\eta )</math> and <math>\sigma =\tfrac{1}{\beta }</math> [[Appendix: Weibull References|[32]]].</div></td></tr>
</table>
Nicolette Young
https://www.reliawiki.com/index.php?title=Template:Characteristics_of_the_gumbel_distribution&diff=21256&oldid=prev
Nicolette Young: /* Characteristics of the Gumbel Distribution */
2012-03-15T17:17:08Z
<p><span class="autocomment">Characteristics of the Gumbel Distribution</span></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 17:17, 15 March 2012</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l7">Line 7:</td>
<td colspan="2" class="diff-lineno">Line 7:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* As <math>\mu </math> increases, the <math>pdf</math> is shifted to the right.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* As <math>\mu </math> increases, the <math>pdf</math> is shifted to the right.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></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>[[Image:<del style="font-weight: bold; text-decoration: none;">effectofmuongumbel</del>.<del style="font-weight: bold; text-decoration: none;">gif|thumb</del>|center|400px| ]] </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>[[Image:<ins style="font-weight: bold; text-decoration: none;">WB</ins>.<ins style="font-weight: bold; text-decoration: none;">16 gumbel pdf.png</ins>|center|400px| ]] </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* As <math>\sigma </math> increases, the <math>pdf</math> spreads out and becomes shallower.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* As <math>\sigma </math> increases, the <math>pdf</math> spreads out and becomes shallower.</div></td></tr>
<tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l13">Line 13:</td>
<td colspan="2" class="diff-lineno">Line 13:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* For <math>T=\pm \infty ,</math> <math>pdf=0.</math> For <math>T=\mu </math> , the <math>pdf</math> reaches its maximum point <math>\frac{1}{\sigma e}</math></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* For <math>T=\pm \infty ,</math> <math>pdf=0.</math> For <math>T=\mu </math> , the <math>pdf</math> reaches its maximum point <math>\frac{1}{\sigma e}</math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></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>[[Image:<del style="font-weight: bold; text-decoration: none;">effectofsigmaongumbel</del>.<del style="font-weight: bold; text-decoration: none;">gif|thumb</del>|center|400px| ]] </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>[[Image:<ins style="font-weight: bold; text-decoration: none;">WB</ins>.<ins style="font-weight: bold; text-decoration: none;">16 effect of sigma.png</ins>|center|400px| ]] </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* The points of inflection of the <math>pdf</math> graph are <math>T=\mu \pm \sigma \ln (\tfrac{3\pm \sqrt{5}}{2})</math> or <math>T\approx \mu \pm \sigma 0.96242</math> .</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* The points of inflection of the <math>pdf</math> graph are <math>T=\mu \pm \sigma \ln (\tfrac{3\pm \sqrt{5}}{2})</math> or <math>T\approx \mu \pm \sigma 0.96242</math> .</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* If times follow the Weibull distribution, then the logarithm of times follow a Gumbel distribution. If <math>{{t}_{i}}</math> follows a Weibull distribution with <math>\beta </math> and <math>\eta </math> , then the <math>Ln({{t}_{i}})</math> follows a Gumbel distribution with <math>\mu =\ln (\eta )</math> and <math>\sigma =\tfrac{1}{\beta }</math> [[Appendix: Weibull References|[32]]].</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* If times follow the Weibull distribution, then the logarithm of times follow a Gumbel distribution. If <math>{{t}_{i}}</math> follows a Weibull distribution with <math>\beta </math> and <math>\eta </math> , then the <math>Ln({{t}_{i}})</math> follows a Gumbel distribution with <math>\mu =\ln (\eta )</math> and <math>\sigma =\tfrac{1}{\beta }</math> [[Appendix: Weibull References|[32]]].</div></td></tr>
</table>
Nicolette Young
https://www.reliawiki.com/index.php?title=Template:Characteristics_of_the_gumbel_distribution&diff=16960&oldid=prev
Harry Guo: /* Characteristics of the Gumbel Distribution */
2012-02-20T18:34:14Z
<p><span class="autocomment">Characteristics of the Gumbel Distribution</span></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 18:34, 20 February 2012</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l16">Line 16:</td>
<td colspan="2" class="diff-lineno">Line 16:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* The points of inflection of the <math>pdf</math> graph are <math>T=\mu \pm \sigma \ln (\tfrac{3\pm \sqrt{5}}{2})</math> or <math>T\approx \mu \pm \sigma 0.96242</math> .</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* The points of inflection of the <math>pdf</math> graph are <math>T=\mu \pm \sigma \ln (\tfrac{3\pm \sqrt{5}}{2})</math> or <math>T\approx \mu \pm \sigma 0.96242</math> .</div></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>:* If times follow the Weibull distribution, then the logarithm of times follow a Gumbel distribution. If <math>{{t}_{i}}</math> follows a Weibull distribution with <math>\beta </math> and <math>\eta </math> , then the <math>Ln({{t}_{i}})</math> follows a Gumbel distribution with <math>\mu =\ln (\eta )</math> and <math>\sigma =\tfrac{1}{\beta }</math> [[Appendix: Weibull References|[32]]] <del style="font-weight: bold; text-decoration: none;"><math></del>.<del style="font-weight: bold; text-decoration: none;"></math></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>:* If times follow the Weibull distribution, then the logarithm of times follow a Gumbel distribution. If <math>{{t}_{i}}</math> follows a Weibull distribution with <math>\beta </math> and <math>\eta </math> , then the <math>Ln({{t}_{i}})</math> follows a Gumbel distribution with <math>\mu =\ln (\eta )</math> and <math>\sigma =\tfrac{1}{\beta }</math> [[Appendix: Weibull References|[32]]].</div></td></tr>
</table>
Harry Guo
https://www.reliawiki.com/index.php?title=Template:Characteristics_of_the_gumbel_distribution&diff=16959&oldid=prev
Harry Guo: /* Characteristics of the Gumbel Distribution */
2012-02-20T18:33:35Z
<p><span class="autocomment">Characteristics of the Gumbel Distribution</span></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 18:33, 20 February 2012</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l16">Line 16:</td>
<td colspan="2" class="diff-lineno">Line 16:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* The points of inflection of the <math>pdf</math> graph are <math>T=\mu \pm \sigma \ln (\tfrac{3\pm \sqrt{5}}{2})</math> or <math>T\approx \mu \pm \sigma 0.96242</math> .</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>:* The points of inflection of the <math>pdf</math> graph are <math>T=\mu \pm \sigma \ln (\tfrac{3\pm \sqrt{5}}{2})</math> or <math>T\approx \mu \pm \sigma 0.96242</math> .</div></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>:* If times follow the Weibull distribution, then the logarithm of times follow a Gumbel distribution. If <math>{{t}_{i}}</math> follows a Weibull distribution with <math>\beta </math> and <math>\eta </math> , then the <math>Ln({{t}_{i}})</math> follows a Gumbel distribution with <math>\mu =\ln (\eta )</math> and <math>\sigma =\tfrac{1}{\beta }</math> [32] <math>.</math></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>:* If times follow the Weibull distribution, then the logarithm of times follow a Gumbel distribution. If <math>{{t}_{i}}</math> follows a Weibull distribution with <math>\beta </math> and <math>\eta </math> , then the <math>Ln({{t}_{i}})</math> follows a Gumbel distribution with <math>\mu =\ln (\eta )</math> and <math>\sigma =\tfrac{1}{\beta }</math> <ins style="font-weight: bold; text-decoration: none;">[[Appendix: Weibull References|</ins>[32<ins style="font-weight: bold; text-decoration: none;">]]</ins>] <math>.</math></div></td></tr>
</table>
Harry Guo
https://www.reliawiki.com/index.php?title=Template:Characteristics_of_the_gumbel_distribution&diff=16958&oldid=prev
Harry Guo: /* Characteristics of the Gumbel Distribution */
2012-02-20T18:31:57Z
<p><span class="autocomment">Characteristics of the Gumbel Distribution</span></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 18:31, 20 February 2012</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l2">Line 2:</td>
<td colspan="2" class="diff-lineno">Line 2:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Some of the specific characteristics of the Gumbel distribution are the following:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Some of the specific characteristics of the Gumbel distribution are the following:</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></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;">• </del>The shape of the Gumbel distribution is skewed to the left. The Gumbel <math>pdf</math> has no shape parameter. This means that the Gumbel <math>pdf</math> has only one shape, which does not change.</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;">* </ins>The shape of the Gumbel distribution is skewed to the left. The Gumbel <math>pdf</math> has no shape parameter. This means that the Gumbel <math>pdf</math> has only one shape, which does not change.</div></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;">• </del>The Gumbel <math>pdf</math> has location parameter <math>\mu ,</math> which is equal to the mode <math>\tilde{T},</math> but it differs from median and mean. This is because the Gumbel distribution is not symmetrical about its <math>\mu </math> .</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;">* </ins>The Gumbel <math>pdf</math> has location parameter <math>\mu ,</math> which is equal to the mode <math>\tilde{T},</math> but it differs from median and mean. This is because the Gumbel distribution is not symmetrical about its <math>\mu </math> .</div></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;">• </del>As <math>\mu </math> decreases, the <math>pdf</math> is shifted to the left.</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;">* </ins>As <math>\mu </math> decreases, the <math>pdf</math> is shifted to the left.</div></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;">• </del>As <math>\mu </math> increases, the <math>pdf</math> is shifted to the right.</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;">* </ins>As <math>\mu </math> increases, the <math>pdf</math> is shifted to the right.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Image:effectofmuongumbel.gif|thumb|center|400px| ]] </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Image:effectofmuongumbel.gif|thumb|center|400px| ]] </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></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;">• </del>As <math>\sigma </math> increases, the <math>pdf</math> spreads out and becomes shallower.</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;">* </ins>As <math>\sigma </math> increases, the <math>pdf</math> spreads out and becomes shallower.</div></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;">• </del>As <math>\sigma </math> decreases, the <math>pdf</math> becomes taller and narrower.</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;">* </ins>As <math>\sigma </math> decreases, the <math>pdf</math> becomes taller and narrower.</div></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;">• </del>For <math>T=\pm \infty ,</math> <math>pdf=0.</math> For <math>T=\mu </math> , the <math>pdf</math> reaches its maximum point <math>\frac{1}{\sigma e}</math></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;">* </ins>For <math>T=\pm \infty ,</math> <math>pdf=0.</math> For <math>T=\mu </math> , the <math>pdf</math> reaches its maximum point <math>\frac{1}{\sigma e}</math></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Image:effectofsigmaongumbel.gif|thumb|center|400px| ]] </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>[[Image:effectofsigmaongumbel.gif|thumb|center|400px| ]] </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></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;">• </del>The points of inflection of the <math>pdf</math> graph are <math>T=\mu \pm \sigma \ln (\tfrac{3\pm \sqrt{5}}{2})</math> or <math>T\approx \mu \pm \sigma 0.96242</math> .</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;">* </ins>The points of inflection of the <math>pdf</math> graph are <math>T=\mu \pm \sigma \ln (\tfrac{3\pm \sqrt{5}}{2})</math> or <math>T\approx \mu \pm \sigma 0.96242</math> .</div></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;">• </del>If times follow the Weibull distribution, then the logarithm of times follow a Gumbel distribution. If <math>{{t}_{i}}</math> follows a Weibull distribution with <math>\beta </math> and <math>\eta </math> , then the <math>Ln({{t}_{i}})</math> follows a Gumbel distribution with <math>\mu =\ln (\eta )</math> and <math>\sigma =\tfrac{1}{\beta }</math> [32] <math>.</math></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;">* </ins>If times follow the Weibull distribution, then the logarithm of times follow a Gumbel distribution. If <math>{{t}_{i}}</math> follows a Weibull distribution with <math>\beta </math> and <math>\eta </math> , then the <math>Ln({{t}_{i}})</math> follows a Gumbel distribution with <math>\mu =\ln (\eta )</math> and <math>\sigma =\tfrac{1}{\beta }</math> [32] <math>.</math></div></td></tr>
</table>
Harry Guo
https://www.reliawiki.com/index.php?title=Template:Characteristics_of_the_gumbel_distribution&diff=16924&oldid=prev
Harry Guo at 18:07, 20 February 2012
2012-02-20T18:07:37Z
<p></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 18:07, 20 February 2012</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;">=</del>==Characteristics of the Gumbel Distribution<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>==Characteristics of the Gumbel Distribution==</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Some of the specific characteristics of the Gumbel distribution are the following:</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Some of the specific characteristics of the Gumbel distribution are the following:</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
</table>
Harry Guo
https://www.reliawiki.com/index.php?title=Template:Characteristics_of_the_gumbel_distribution&diff=11179&oldid=prev
Nicolette Young: Created page with '===Characteristics of the Gumbel Distribution=== Some of the specific characteristics of the Gumbel distribution are the following: :• The shape of the Gumbel distribution is …'
2012-01-04T22:50:24Z
<p>Created page with '===Characteristics of the Gumbel Distribution=== Some of the specific characteristics of the Gumbel distribution are the following: :• The shape of the Gumbel distribution is …'</p>
<p><b>New page</b></p><div>===Characteristics of the Gumbel Distribution===<br />
Some of the specific characteristics of the Gumbel distribution are the following:<br />
<br />
:• The shape of the Gumbel distribution is skewed to the left. The Gumbel <math>pdf</math> has no shape parameter. This means that the Gumbel <math>pdf</math> has only one shape, which does not change.<br />
:• The Gumbel <math>pdf</math> has location parameter <math>\mu ,</math> which is equal to the mode <math>\tilde{T},</math> but it differs from median and mean. This is because the Gumbel distribution is not symmetrical about its <math>\mu </math> .<br />
:• As <math>\mu </math> decreases, the <math>pdf</math> is shifted to the left.<br />
:• As <math>\mu </math> increases, the <math>pdf</math> is shifted to the right.<br />
<br />
[[Image:effectofmuongumbel.gif|thumb|center|400px| ]] <br />
<br />
:• As <math>\sigma </math> increases, the <math>pdf</math> spreads out and becomes shallower.<br />
:• As <math>\sigma </math> decreases, the <math>pdf</math> becomes taller and narrower.<br />
:• For <math>T=\pm \infty ,</math> <math>pdf=0.</math> For <math>T=\mu </math> , the <math>pdf</math> reaches its maximum point <math>\frac{1}{\sigma e}</math><br />
<br />
[[Image:effectofsigmaongumbel.gif|thumb|center|400px| ]] <br />
<br />
:• The points of inflection of the <math>pdf</math> graph are <math>T=\mu \pm \sigma \ln (\tfrac{3\pm \sqrt{5}}{2})</math> or <math>T\approx \mu \pm \sigma 0.96242</math> .<br />
:• If times follow the Weibull distribution, then the logarithm of times follow a Gumbel distribution. If <math>{{t}_{i}}</math> follows a Weibull distribution with <math>\beta </math> and <math>\eta </math> , then the <math>Ln({{t}_{i}})</math> follows a Gumbel distribution with <math>\mu =\ln (\eta )</math> and <math>\sigma =\tfrac{1}{\beta }</math> [32] <math>.</math></div>
Nicolette Young