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I'm a student learning about methods for generating random variables.

But I'm having a hard time finding examples or youtube tutorials on composition method and algorithm of generating random variables.

Given that this method is grouped with Acceptance-Rejection and inverse transform in the lecture notes my prof handed out, I'd imagine it is a rather common method. So I was wondering whether it is referred to with a different name more commonly? Because I had to no trouble finding examples and tutorials for the A-R and I-T methods.

Obviously my prof's lectures/office hours aren't very helpful and this method isn't even in the textbook. There are no solved examples on this and multiple questions in the homework. Only a single slide in the notes.

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I even searched for different methods of generating RVs (https://www.encyclopediaofmath.org/index.php/Generating_random_variables) But it seems to not exist.

Kal
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  • You would use a method such as acceptance-rejection or inverse transform to generate the random variates $X_1,\ldots,X_n$. – Math1000 Mar 09 '20 at 23:48
  • @Math1000 that is not the question here. This does not answer my question. – Kal Mar 10 '20 at 00:17
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    It does, actually. If you understand how to generate the random variates using the other methods, then the straightforward algorithm that you have posted tells you exactly how to generate a random variate using this method. – Math1000 Mar 10 '20 at 01:37
  • @Math1000 again, that is not the question. Please refer to the post. I am asking for information on this method. – Kal Mar 10 '20 at 02:40
  • @Math1000 your comment does not answer the question stated in the post. – Kal Mar 10 '20 at 02:41
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    Try searching for "mixture distribution" then. That's all this is. It seems like you're overthinking this. The algorithm here is very straightforward and cannot be explained any more simply than how you posted it in your question. – Math1000 Mar 10 '20 at 03:49

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