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<p class="MsoNormal">Hello Sergey,</p>
<p class="MsoNormal">Many t<span lang="EN-US">hanks for your
answer. Re-using the vocabulary of [1]: indeed the alias
method [2] that you chose looks very relevant when having a
distribution of discrete (rather than continuous)
probabilities (and this must be a lot simpler and more
efficient than explicitly transforming a probability density
function [3] into a cumulative distribution one [4],
approximating its inverse and drawing uniformly from it).</span></p>
<p class="MsoNormal"><span lang="EN-US">The implementation looks
quite functional to me! The use of the array module seems
difficult to avoid. The precomputed term must remain quite
small. Then, as expected, two uniform draws are necessary per
sample generation; looks very reasonable. Maybe
<span class="pl-en">replacing calls to crypto</span>:<span
class="pl-en">rand_uniform/2 by calls to rand:uniform/1
could be relevant?</span></span></p>
<p class="MsoNormal"><span class="pl-en"><span lang="EN-US">Weights
could be I guess typed as number() rather than integer() (so
that they include probabilities already normalized in [0.0,
1.0]) with no special change in the actual code.</span></span><span
lang="EN-US"></span></p>
<p class="MsoNormal"><span lang="EN-US">Many thanks for sharing
such a clear, referenced and compact implementation - much
appreciated!
</span></p>
<p class="MsoNormal"><span lang="EN-US">Best regards,</span></p>
<p class="MsoNormal"><span lang="EN-US">Olivier.</span></p>
<p class="MsoNormal"><span lang="EN-US"> </span></p>
<p class="MsoNormal"><span lang="EN-US">[1] <a
href="https://en.wikipedia.org/wiki/Inverse_transform_sampling"
class="moz-txt-link-freetext">
https://en.wikipedia.org/wiki/Inverse_transform_sampling</a></span></p>
<p class="MsoNormal"><span lang="EN-US">[2] <a
href="https://en.wikipedia.org/wiki/Alias_method"
class="moz-txt-link-freetext">
https://en.wikipedia.org/wiki/Alias_method</a></span></p>
<p class="MsoNormal"><span lang="EN-US">[3] <a
href="https://en.wikipedia.org/wiki/Probability_density_function"
class="moz-txt-link-freetext">
https://en.wikipedia.org/wiki/Probability_density_function</a></span></p>
<p class="MsoNormal"><span lang="EN-US">[4] <a
href="https://en.wikipedia.org/wiki/Cumulative_distribution_function"
class="moz-txt-link-freetext">
https://en.wikipedia.org/wiki/Cumulative_distribution_function</a></span></p>
<p class="MsoNormal"><span lang="EN-US"> <br>
</span></p>
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<div class="moz-cite-prefix">Le 1/25/22 à 14:56, Sergey Prokhorov a
écrit :<br>
</div>
<blockquote type="cite"
cite="mid:CAMZozm7FNF7_7iyVjFC-M+_aHE7=AmMxNddzbyeXeniWYVU5vg@mail.gmail.com">
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<div>Hi,</div>
<div><br>
</div>
<div>I'm not sure I fully understand the terminology, but did I
understand correctly that you are looking for some "random
choice with weights"?</div>
<div><br>
</div>
<div>I have implemented the "walker alias" algorithm some time
ago</div>
<div><a href="https://gist.github.com/seriyps/5593193"
moz-do-not-send="true" class="moz-txt-link-freetext">https://gist.github.com/seriyps/5593193</a></div>
<div>But it is more or less a direct translation from imperative
code, so it does not look really idiomatic.</div>
<div>And it also only returns values from a predefined finite
set, not via arbitrary density function.<br>
</div>
<div> </div>
<blockquote class="gmail_quote" style="margin:0px 0px 0px
0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">Hi,<br>
<br>
A bit in link with the recent message of Kenji regarding <br>
state-of-the-art random generators: if needing to draw samples
from, <br>
this time, a specific, non-uniform distribution, are there
Erlang <br>
libraries able to accept as input such a user-specified,
arbitrary <br>
probability density function?<br>
<br>
(I searched for "Inverse transform sampling in Erlang" and
alike, yet, <br>
because of the statistical distribution of the same name,
pointers are <br>
difficult to find)<br>
<br>
Thanks in advance for any information,<br>
<br>
Best regards,<br>
<br>
Olivier.<br>
<br>
-- <br>
<br>
Olivier Boudeville</blockquote>
</div>
</blockquote>
<p><br>
</p>
<pre class="moz-signature" cols="72">--
Olivier Boudeville
</pre>
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