<div dir="ltr"><div>Hi Michael,</div><div><br></div><div>Not sure I can help on this. I am not very knowledgeable on MLE or GEV <br></div><div><br></div><div>As noted in the documentation, NCL invokes a August 1994 version of:<br></div><div><br></div><div>Algorithm 215: Maximum-Likelihood Estimation of the Parameters of the Generalized Extreme-Value Distribution</div><div><pre>J. R. M. Hosking
Journal of the Royal Statistical Society. Series C (Applied Statistics)
Vol. 34, No. 3 (1985), pp. 301-310
URL: <a href="http://www.jstor.org/stable/2347483">http://www.jstor.org/stable/2347483</a>
Code: <a href="http://ftp.uni-bayreuth.de/math/statlib/apstat/215"><b>http://ftp.uni-bayreuth.de/math/statlib/apstat/215</b></a><br><br></pre><pre>My recollection is that we tested this on a few 'book' examples and compared the output to results generated by R's <b>gev.fit </b>function<b>.<br><br>====<br></b></pre><pre><a href="https://www.ncl.ucar.edu/Document/Functions/Built-in/extval_mlegev.shtml"><b>extval_mlegev</b></a>: Example 1 illustrates a comparison. I believe you have used R. Perhaps trying your data using R <br>will provide another (NCL, MATLAB) viewpoint.<br><br>====<br></pre><pre>Again, I am not very knowledgeable on either MLE or GEV so I have no idea what the -1 does within the algorithm.<br><br></pre><pre>Regards<br></pre><pre>D<br></pre><pre><b><br></b>
</pre></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Tue, Nov 16, 2021 at 3:24 PM Michael Notaro via ncl-talk <<a href="mailto:ncl-talk@mailman.ucar.edu">ncl-talk@mailman.ucar.edu</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
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In the example below, I have 20 values of precipitation in inches.</div>
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Each value is the highest daily precipitation for one of 20 years.</div>
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I want to estimate the 1-day/100-year GEV precipitation level.</div>
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For some reason, my older script included multiplying the shape</div>
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parameter by -1. That gave a GEV value of 65757", definitely wrong.</div>
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If I get rid of the *-1 part, the GEV value becomes more reasonable,</div>
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1.73", but too low compared to the 20 annual max values. So I have</div>
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two questions.</div>
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<ol>
<li>Is there something wrong with the script below?<span></span></li><li>Is there ever a need to multiply any of the parameters by -1? I</li><li style="display:block">did it once before but have no recollection of why I did it.</li></ol>
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Thanks, Michael</div>
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yearmax=(/1.83,1.69,3.24,1.99,1.69,1.79,2.78,1.70,4.85,2.35,3.37,1.72,3.96,2.35,2.29,3.33,3.97,3.53,3.11,1.69/)
<div>param=extval_mlegev(yearmax,0,False)</div>
<div>param_mle_location=param(0)</div>
<div>param_mle_scale=param(1)</div>
<div>param_mle_shape=param(2)*-1.</div>
<div>coeff=-1.*log(1.-1./100.)</div>
<div>gev=param_mle_scale/param_mle_shape*[coeff^(-1.*param_mle_shape)-1.]+param_mle_location</div>
<span>print("param_mle_location="+param_mle_location+" param_mle_scale="+param_mle_scale+" param_mle_shape="+param_mle_shape+" coeff="+coeff+" gev= "+gev)</span><br>
</div>
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<span><br>
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<span style="background-color:rgb(255,255,0)">param_mle_location=1.65715 param_mle_scale=0.216018 param_mle_shape=2.98224 coeff=0.0100503 gev= 65757.5</span><span><br>
</span></div>
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<span><br>
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<span><span style="background-color:rgb(255,255,255);display:inline">earmax=(/1.83,1.69,3.24,1.99,1.69,1.79,2.78,1.70,4.85,2.35,3.37,1.72,3.96,2.35,2.29,3.33,3.97,3.53,3.11,1.69/)</span>
<div style="margin:0px;background-color:rgb(255,255,255)">param=extval_mlegev(yearmax,0,False)</div>
<div style="margin:0px;background-color:rgb(255,255,255)">param_mle_location=param(0)</div>
<div style="margin:0px;background-color:rgb(255,255,255)">param_mle_scale=param(1)</div>
<div style="margin:0px;background-color:rgb(255,255,255)">param_mle_shape=param(2)*-1.</div>
<div style="margin:0px;background-color:rgb(255,255,255)">coeff=-1.*log(1.-1./100.)</div>
<div style="margin:0px;background-color:rgb(255,255,255)">gev=param_mle_scale/param_mle_shape*[coeff^(-1.*param_mle_shape)-1.]+param_mle_location</div>
<span style="margin:0px;background-color:rgb(255,255,255)">print("param_mle_location="+param_mle_location+" param_mle_scale="+param_mle_scale+" param_mle_shape="+param_mle_shape+" coeff="+coeff+" gev= "+gev)</span><br>
</span></div>
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<span><span style="margin:0px;background-color:rgb(255,255,255)"><br>
</span></span></div>
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<span><span style="margin:0px;background-color:rgb(255,255,0)">param_mle_location=1.65715 param_mle_scale=0.216018 param_mle_shape=-2.98224 coeff=0.0100503 gev= 1.72958</span><span style="margin:0px;background-color:rgb(255,255,255)"><br>
</span></span></div>
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<div id="gmail-m_4840502285418351531Signature">
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<div id="gmail-m_4840502285418351531divtagdefaultwrapper" style="font-size:12pt;color:rgb(0,0,0);background-color:rgb(255,255,255);font-family:Calibri,Arial,Helvetica,sans-serif">
Michael Notaro<br>
<div>Associate Director<br>
</div>
<div>Nelson Institute Center for Climatic Research<br>
</div>
<div>University of Wisconsin-Madison<br>
</div>
<div>Phone: (608) 261-1503<br>
</div>
<div>Email: <a href="mailto:mnotaro@wisc.edu" target="_blank">mnotaro@wisc.edu</a><br>
</div>
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</div>
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