<html><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">On 04.11.2022, at 09:46, Dang Ngoc Chan, Christophe <<a href="mailto:Christophe.Dang@sidel.com" class="">Christophe.Dang@sidel.com</a>> wrote:<br class=""><blockquote type="cite" class=""><br class="">Hello Heinz,<br class=""><br class=""><blockquote type="cite" class="">De : users <<a href="mailto:users-bounces@lists.scilab.org" class="">users-bounces@lists.scilab.org</a>> De la part de Heinz Nabielek<br class="">Envoyé : mardi 1 novembre 2022 22:02<br class=""><br class="">I need to compute the inverse of the cumulative beta function, but I just cannot handle cdfbet.<br class=""></blockquote><br class="">From what I undestand in<br class=""><a href="https://help.scilab.org/docs/6.1.1/en_US/cdfbet.html" class="">https://help.scilab.org/docs/6.1.1/en_US/cdfbet.html</a><br class="">the notation for the beta function in Scilab is :<br class="">P = \int_{0}^{X} t^{A-1} * (1-t)^{B-1} dt<br class="">What you want is X knowing [P, A, B] right ?<br class="">The syntax seems to be<br class="">[X,Y]=cdfbet("XY",A,B,P,Q)<br class="">With Q = 1 - P.<br class="">With your examples:<br class="">--> [X,Y]=cdfbet("XY",1 ,10 ,0.95 ,0.05)<br class="">X = 0.2588656<br class="">Y = 0.7411344<br class="">--> [X,Y]=cdfbet("XY",1 ,100 ,0.95 ,0.05)<br class="">X = 0.0295130<br class="">Y = 0.9704870<br class=""><br class="">Regards<br class="">Christophe Dang Ngoc Chan<br class=""></blockquote><br class=""><br class=""><div class=""><br class=""></div><div class="">Dear Christophe et Stéphane,<br class="">great many thanks for the patient explanations.</div><div class="">This way I was able to compute acceptance limits in the large-scale manufacture of small objects that are difficult to find in textbooks.</div><div class="">Greetings</div><div class="">Heinz ... I am certain that you can generate a much more efficient Scilab code.</div><div class=""><br class=""></div><div class=""><pre class=""><font face="Times" class=""><span style="font-style: normal; font-size: 18px;" class="">N<span style="color: rgb(92, 92, 92);" class="">=</span><span style="color: rgb(188, 143, 143);" class="">10</span><span style="color: rgb(92, 92, 92);" class="">^</span><span style="color: rgb(74, 85, 219);" class="">(</span><span style="color: rgb(188, 143, 143);" class="">3</span><span style="color: rgb(255, 170, 0);" class="">:</span><span style="color: rgb(188, 143, 143);" class="">9</span><span style="color: rgb(74, 85, 219);" class="">)</span>;
def<span style="color: rgb(92, 92, 92);" class="">=</span><span style="color: rgb(74, 85, 219);" class="">[</span><span style="color: rgb(188, 143, 143);" class="">300</span> <span style="color: rgb(188, 143, 143);" class="">100</span> <span style="color: rgb(188, 143, 143);" class="">30</span> <span style="color: rgb(188, 143, 143);" class="">10</span> <span style="color: rgb(188, 143, 143);" class="">3</span> <span style="color: rgb(188, 143, 143);" class="">1</span> <span style="color: rgb(188, 143, 143);" class="">0</span><span style="color: rgb(74, 85, 219);" class="">]</span>;
<span style="color: rgb(160, 32, 240);" class="">for</span> i<span style="color: rgb(92, 92, 92);" class="">=</span><span style="color: rgb(188, 143, 143);" class="">1</span><span style="color: rgb(255, 170, 0);" class="">:</span><span style="color: rgb(188, 143, 143);" class="">7</span>;
NN<span style="color: rgb(92, 92, 92);" class="">=</span>N<span style="color: rgb(74, 85, 219);" class="">(</span>i<span style="color: rgb(74, 85, 219);" class="">)</span>;
<span style="color: rgb(160, 32, 240);" class="">for</span> j<span style="color: rgb(92, 92, 92);" class="">=</span><span style="color: rgb(188, 143, 143);" class="">1</span><span style="color: rgb(255, 170, 0);" class="">:</span><span style="color: rgb(188, 143, 143);" class="">7</span>;
defects<span style="color: rgb(92, 92, 92);" class="">=</span>def<span style="color: rgb(74, 85, 219);" class="">(</span>j<span style="color: rgb(74, 85, 219);" class="">)</span>;
A<span style="color: rgb(74, 85, 219);" class="">(</span>i,j<span style="color: rgb(74, 85, 219);" class="">)</span><span style="color: rgb(92, 92, 92);" class="">=</span><span style="color: rgb(50, 185, 185);" class="">cdfbet</span><span style="color: rgb(74, 85, 219);" class="">(</span><span style="color: rgb(188, 143, 143);" class="">"</span><span style="color: rgb(188, 143, 143);" class="">XY</span><span style="color: rgb(188, 143, 143);" class="">"</span>, defects<span style="color: rgb(92, 92, 92);" class="">+</span><span style="color: rgb(188, 143, 143);" class="">1</span>, NN<span style="color: rgb(92, 92, 92);" class="">+</span><span style="color: rgb(188, 143, 143);" class="">1</span><span style="color: rgb(92, 92, 92);" class="">-</span>defects, <span style="color: rgb(188, 143, 143);" class="">.95</span>,<span style="color: rgb(188, 143, 143);" class="">.05</span><span style="color: rgb(74, 85, 219);" class="">)</span>;
<span style="color: rgb(160, 32, 240);" class="">end</span>;
<span style="color: rgb(50, 185, 185);" class="">plot2d</span><span style="color: rgb(74, 85, 219);" class="">(</span><span style="color: rgb(188, 143, 143);" class="">1e9</span>,<span style="color: rgb(188, 143, 143);" class="">1</span>,logflag<span style="color: rgb(92, 92, 92);" class="">=</span><span style="color: rgb(188, 143, 143);" class="">'</span><span style="color: rgb(188, 143, 143);" class="">ll</span><span style="color: rgb(188, 143, 143);" class="">'</span><span style="color: rgb(74, 85, 219);" class="">)</span>;<span style="color: rgb(50, 185, 185);" class="">xgrid</span><span style="color: rgb(74, 85, 219);" class="">(</span><span style="color: rgb(74, 85, 219);" class="">)</span>;
<span style="color: rgb(174, 92, 176); text-decoration: underline;" class="">plot</span><span style="color: rgb(74, 85, 219);" class="">(</span>N<span style="color: rgb(92, 92, 92);" class="">'</span>, A,<span style="color: rgb(188, 143, 143);" class="">'</span><span style="color: rgb(188, 143, 143);" class="">--</span><span style="color: rgb(188, 143, 143);" class="">'</span>,<span style="color: rgb(188, 143, 143);" class="">'</span><span style="color: rgb(188, 143, 143);" class="">LineWidth</span><span style="color: rgb(188, 143, 143);" class="">'</span>,<span style="color: rgb(188, 143, 143);" class="">3</span><span style="color: rgb(74, 85, 219);" class="">)</span>;
a<span style="color: rgb(92, 92, 92);" class="">=</span><span style="color: rgb(174, 92, 176); text-decoration: underline;" class="">gca</span><span style="color: rgb(74, 85, 219);" class="">(</span><span style="color: rgb(74, 85, 219);" class="">)</span>;a<span style="color: rgb(92, 92, 92);" class="">.</span><span style="color: rgb(170, 170, 170);" class="">font_size</span><span style="color: rgb(92, 92, 92);" class="">=</span><span style="color: rgb(188, 143, 143);" class="">3</span>;
<span style="color: rgb(174, 92, 176); text-decoration: underline;" class="">legend</span> <span style="color: rgb(74, 85, 219);" class="">(</span><span style="color: rgb(188, 143, 143);" class="">'</span><span style="color: rgb(188, 143, 143);" class="">n=</span><span style="color: rgb(188, 143, 143);" class="">'</span>,<span style="color: rgb(188, 143, 143);" class="">'</span><span style="color: rgb(188, 143, 143);" class="">300 defects</span><span style="color: rgb(188, 143, 143);" class="">'</span>,<span style="color: rgb(188, 143, 143);" class="">'</span><span style="color: rgb(188, 143, 143);" class="">100 defects</span><span style="color: rgb(188, 143, 143);" class="">'</span>,<span style="color: rgb(188, 143, 143);" class="">'</span><span style="color: rgb(188, 143, 143);" class="">30 defects</span><span style="color: rgb(188, 143, 143);" class="">'</span>,<span style="color: rgb(188, 143, 143);" class="">'</span><span style="color: rgb(188, 143, 143);" class="">10 defects</span><span style="color: rgb(188, 143, 143);" class="">'</span>,<span style="color: rgb(188, 143, 143);" class="">'</span><span style="color: rgb(188, 143, 143);" class="">3 defects</span><span style="color: rgb(188, 143, 143);" class="">'</span>,<span style="color: rgb(188, 143, 143);" class="">'</span><span style="color: rgb(188, 143, 143);" class="">1 defect</span><span style="color: rgb(188, 143, 143);" class="">'</span>,<span style="color: rgb(188, 143, 143);" class="">'</span><span style="color: rgb(188, 143, 143);" class="">0 defects</span><span style="color: rgb(188, 143, 143);" class="">'</span><span style="color: rgb(74, 85, 219);" class="">)</span>;
<span style="color: rgb(174, 92, 176); text-decoration: underline;" class="">xlabel</span><span style="color: rgb(74, 85, 219);" class="">(</span><span style="color: rgb(188, 143, 143);" class="">'</span><span style="color: rgb(188, 143, 143);" class="">N = number of particles investiged</span><span style="color: rgb(188, 143, 143);" class="">'</span>,<span style="color: rgb(188, 143, 143);" class="">'</span><span style="color: rgb(188, 143, 143);" class="">fontsize</span><span style="color: rgb(188, 143, 143);" class="">'</span>,<span style="color: rgb(188, 143, 143);" class="">3</span><span style="color: rgb(74, 85, 219);" class="">)</span>;
<span style="color: rgb(174, 92, 176); text-decoration: underline;" class="">ylabel</span><span style="color: rgb(74, 85, 219);" class="">(</span><span style="color: rgb(188, 143, 143);" class="">'</span><span style="color: rgb(188, 143, 143);" class="">one-sided upper 95% defect fraction</span><span style="color: rgb(188, 143, 143);" class="">'</span>,<span style="color: rgb(188, 143, 143);" class="">'</span><span style="color: rgb(188, 143, 143);" class="">fontsize</span><span style="color: rgb(188, 143, 143);" class="">'</span>,<span style="color: rgb(188, 143, 143);" class="">3</span><span style="color: rgb(74, 85, 219);" class="">)</span>;
<span style="color: rgb(174, 92, 176); text-decoration: underline;" class="">title</span> <span style="color: rgb(74, 85, 219);" class="">(</span><span style="color: rgb(188, 143, 143);" class="">'</span><span style="color: rgb(188, 143, 143);" class="">Acceptance limit of defect fraction n/N at 95% confidence</span><span style="color: rgb(188, 143, 143);" class="">'</span>,<span style="color: rgb(188, 143, 143);" class="">'</span><span style="color: rgb(188, 143, 143);" class="">fontsize</span><span style="color: rgb(188, 143, 143);" class="">'</span>,<span style="color: rgb(188, 143, 143);" class="">4</span><span style="color: rgb(74, 85, 219);" class="">)</span>;</span></font></pre><div class=""><br class=""></div></div><div class=""><br class=""><br class=""></div></body></html>