[RFC]: Implement a broader range of statistical distributions

[Md-Zaid45]

Full name

Moh Zaid Khan

University status

Yes

University name

Madhav Institute of Technology and Science, Gwalior

University program

B.Tech in Mathematics and Computing

Expected graduation

June 2027

Short biography

I am Moh Zaid Khan, a third year Mathematics and Computing student at MITS Gwalior. I enjoy implementing Mathematics to solve real world problems. Through my degree curriculum, I have built a strong foundation in advanced mathematics and programming using C, C++, and Python. Recently I have been working on personal Full-Stack project in MERN stack. Therefore, I have all prerequisite skills to work on challenges in this proposal

Timezone

IST (UTC +5:30)

Contact details

mz1944680@gmail.com

Platform

Windows

Editor

I use VSCode. It is fast and the integrated terminal keeps my workflow centralized

Programming experience

I've been building full-stack web apps with a strong focus on algorithmic logic. Recently, I built Noto, a full-stack notes and flashcard application. For scheduling Flashcards, I wrote a custom implementation of the SM-2 Spaced Repetition algorithm in pure JavaScript, which calculates dynamic review intervals using exponential math based on user recall data.

JavaScript experience

I write a lot of JS for both the frontend and backend.

Favorite feature: I really like its asynchronous model and first-class functions it makes writing functional, event-driven code very natural.

Least favorite feature: Implicit type coercion. When writing numerical algorithms, having JS silently propagate NaN or coerce types instead of throwing an error makes debugging incredibly frustrating.

Node.js experience

I use Node.js for my backend projects. I'm comfortable with package management, the CommonJS/ESM module systems, and writing asynchronous scripts for file system operations.

C/Fortran experience

My university coursework involves writing C for Data Structures and Algorithm Design. I am comfortable with static typing, manual memory management.

Interest in stdlib

I really appreciate how @stdlib brings the mathematical rigor you usually only see in C or Python over to the JavaScript ecosystem. This makes developers to use JavaScript for Statistics, Data Analysis, Machine Learning, or other Mathematical applications

Version control

Yes

Contributions to stdlib

PR #11232: Fixed wrong header filename in @stdlib/math/base/special/fast/pow-int
renamed pow.h to pow_int.h to match the package name.
[Status: Open]

stdlib showcase

I built a Node.js CLI tool that simulates and analyzes spaced-repetition study sessions.

I used @stdlib/random-base-normal to generate mock daily study scores, and then applied @stdlib/stats-base-mean and @stdlib/stats-base-stdev to calculate average retention rates and study consistency over time.

• Showcase Repository: https://github.com/Md-Zaid45/stdlib-flashcard-stats

Goals

My goal is to implement various statistical distributions for @stdlib while ensuring they hold up against extreme edge cases.

Key deliverables:

• Core API: Writing standard methods (PDF, CDF, quantile, and random generation) for each target distribution.
• Numerical Stability: Handling floating point limitations to prevent overflow, underflow, and precision loss at extreme parameter boundaries.
• Performance Optimization: Improving root finding and approximation algorithms to reach machine-level accuracy faster.
• Validation: Testing all code against established libraries like SciPy to guarantee high-precision results.

Why this project?

As a Mathematics and Computing student, this project perfectly aligns with my academic focus and my love for JavaScript. I am excited by the challenge of translating pure mathematical limits.

Qualifications

My university coursework directly supports this work:

Real and Complex Analysis,
Numerical Techniques,
Algorithm Analysis,
Probability and Statistics,
Optimization Techniques,
C/C++/Python.
And I have learned Full-Stack Development in MERN stack, Therefore, I acquire all the prerequisites skills to work on this proposal

Prior art

These distributions are well-established in Python's scipy.stats and C++'s Boost.Math. I plan to use SciPy's source code as a reference for handling edge-cases and use its outputs to generate my JSON test fixtures. R's extRemes package is also a great reference for the GEV and GPD logic.

Commitment

I plan to commit 35-40 hours a week to this project and can extend working hours if needed.

Schedule

Community Bonding (May 1 – May 25)
Commit generate_fixtures.py to establish the testing pipeline. Draft API signatures for the new distributions and review @stdlib sub-package structures to ensure seamless integration.

Weeks 1–2 (May 26 – Jun 8)
Establish JSDoc and benchmarks. Implement the genpareto (GPD) distribution. Focus heavily on implementing Taylor expansions for shape parameter limits.

Weeks 3–4 (Jun 9 – Jun 22)
Implement the genextreme (GEV) distribution. Handle parameter limit continuity and implement Halley's Method for quantile refinement to ensure cubic convergence.

Weeks 5–6 (Jun 23 – Jul 6)
Implement the invgauss distribution. Focus on mitigating log-space floating-point overflow and refining Halley root-finding for edge cases.

Weeks 7–8 (Jul 7 – Jul 20)
Implement the vonmises and rice distributions. The primary focus will be on handling Bessel function log-space expansions to maintain IEEE 754 precision.

Weeks 9–10 (Jul 21 – Aug 3)
Implement the betabinom and skellam distributions. Address and handle combinatorial overflow and recurrence drift typical in these discrete distributions.

Weeks 11–12 (Aug 4 – Aug 25)
Implement the zipf distribution. Run a comprehensive full test pass against all scipy.stats golden fixtures. Complete any stretch goals (e.g., lomax) and address final mentor feedback before submission.

Related issues

N/A

Checklist

• I have read and understood the Code of Conduct.
• I have read and understood the application materials found in this repository.
• I understand that plagiarism will not be tolerated, and I have authored this application in my own words.
• I have read and understood the patch requirement which is necessary for my application to be considered for acceptance.
• I have read and understood the stdlib showcase requirement which is necessary for my application to be considered for acceptance.
• The issue name begins with [RFC]: and succinctly describes your proposal.
• I understand that, in order to apply to be a GSoC contributor, I must submit my final application to https://summerofcode.withgoogle.com/ before the submission deadline.