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:
1. *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.
2. *Algebra of Random Variables*:
- Additionally, I would like to explore algebraic operations
involving random variables, particularly focusing on the *ratio
distribution*.
- Ratio distribution - Wikipedia
<https://en.wikipedia.org/wiki/Ratio_distribution>
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
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