Operations with probability distributions

Question

I had an idea that passes by declaring a new type of computer variable (like Integer, Double, etc.) that represents a statistical probability distribution (PDF), for that I would need to define the basic operations; sum, multiplication, inverse and negation.

The problem is that I have no idea of how to define such operations or if that is even possible. (I'm electrical engineer...)

So the question is; How to sum, multiply, inverse and negate probability distributions, or where can I learn how to do it. A numerical approach would be sufficient.

Thanks.

score 1 · Answer 1 · answered Jun 30 '15 at 18:12

1

This is not trivial. For example density function of sum of two continuous variables is convolution of densities of these variables.

answered Jun 30 '15 at 18:12

mcihak

614
4
12

You can study more about sums of random variables at http://www.dartmouth.edu/~chance/teaching_aids/books_articles/probability_book/Chapter7.pdf – mcihak Jun 30 '15 at 18:15

score 1 · Answer 2 · answered Jun 30 '15 at 18:36

1

A reasonable interpretation of "sum" or "multiply" for two probability distributions is the distribution of the sum or product of two independent random variables with those distributions. However, there's no natural way to have an "inverse".

answered Jun 30 '15 at 18:36

Robert Israel

448,999

Operations with probability distributions

2 Answers2