Hi. I'm not sure if the things you mentioned are implemented or not, but if they are, they would be in the sympy.stats module. If they aren't there yet, it sounds like they would be appropriate for that submodule. sympy.stats implements the algebra of random variables you are talking about. Taking ratios of random variables is supported, although there may be different things that aren't yet implemented.
Also note that some of these things are more general mathematical concepts applied to statistics (like asymptotic expansions), which may already be implemented in other parts of SymPy. For example, there is support for asymptotic expansions (aseries()), although I don't know if Sterling's approximation is implemented. Aaron Meurer On Tue, Apr 23, 2024 at 1:25 PM Matthew Robinson <exaggera...@gmail.com> wrote: > > Dear SymPy Developers Group, > > I hope this email finds you well. I am currently exploring the use of SymPy, > a powerful symbolic mathematics library, to simplify equations related to > mathematical statistics. Specifically, I am interested in developing a > function that can handle statistical equations by recognizing and > substituting large sample size (asymptotic) approximations. > > Here are the key aspects I’d like to address: > > Approximations: > > Sterling’s Approximation: I aim to incorporate Sterling’s Approximation for > factorials, which becomes increasingly accurate for large values. > Binomial and Poisson Distributions: I want to approximate these discrete > distributions with the Normal Distribution when dealing with large sample > sizes. > > Algebra of Random Variables: > > Additionally, I would like to explore algebraic operations involving random > variables, particularly focusing on the ratio distribution. > Ratio distribution - Wikipedia > > In summary, my goal is to input formulas that involve distributions (such as > binomial and Poisson distributions) into SymPy. The library should then > simplify these formulas using well-known large sample size approximations, > including the normal distribution and Sterling’s approximation. For example, > if the ratio of a Poisson Distribution divided by a Binomial Distribution is > input, it should output a mathematically simplified expression representing > the large sample size approximations of the Poisson distribution divided by > the large sample size approximation for the Binomial distribution. > > If there are existing methods or tools for achieving this, I would greatly > appreciate any guidance or pointers. Alternatively, if no such methods > currently exist, I am enthusiastic about contributing to the development of > this functionality. > > Thank you for your time, and I look forward to any insights or suggestions > you may have. > > Best regards, > > Matthew Robinson > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to sympy+unsubscr...@googlegroups.com. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/dde90ce8-95b4-4565-9293-e8392c029110n%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to sympy+unsubscr...@googlegroups.com. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAKgW%3D6LfhZZL87H6QhYO5qMoKEzxNwyVE3ssQ1ahu%3D8UkAnhdw%40mail.gmail.com.
