probplots — DLBDSS01-01 Statistics Helper (CLI + Plots + Joint API)

Course-aligned tools for Probability & Descriptive Statistics (DLBDSS01‑01).
Runs great on Ubuntu and Raspberry Pi 5. Includes closed‑form distribution queries, inequalities/CLT helpers, simulations, headless plotting, and discrete joint-distribution analysis.

Main entry (CLI): /home/zk/projects/probplots/dlbdss
Python API (package): /home/zk/projects/probplots/stats_helper
No need to activate the venv for the CLI; the shebang points to the project’s Python.

Features

Probability basics: factorial, perm, comb
Distributions (PMF/CDF/quantiles): Binomial, Poisson, Geometric, Normal, Exponential, Uniform
Inequalities & theorems: Markov, Chebyshev, CLT (sample‑mean probability on an interval)
Simulations with visual overlays: sim-hist (Normal, Binomial, Poisson)
Headless plots via --out file.png (automatic Agg backend when no DISPLAY)
Joint distributions (discrete): validate joint PMF, marginals, conditionals, independence test, and E, Var, Cov, Corr from a joint table

Project Layout

/home/zk/projects/probplots
├── .venv/
├── bin/
│   └── dlbdss
├── dlbdss                  # convenience launcher (execs bin/dlbdss)
└── stats_helper/
    ├── __init__.py        # exports compute_joint_stats(...)
    └── joint_dist.py      # JointDist class

Install (one‑time)

/usr/bin/mkdir -p /home/zk/projects/probplots/bin
/usr/bin/python3 -m venv /home/zk/projects/probplots/.venv
source /home/zk/projects/probplots/.venv/bin/activate
/home/zk/projects/probplots/.venv/bin/pip install --upgrade pip
/home/zk/projects/probplots/.venv/bin/pip install --only-binary=:all: numpy scipy matplotlib

Usage Cheat‑Sheet (CLI)

# Normal CDF: P(X ≤ 1.96) for N(0,1)
/home/zk/projects/probplots/dlbdss norm-cdf --x 1.96 --mu 0 --sigma 1

# Binomial: P(X = 4) for X~Bin(n=10,p=0.3)
/home/zk/projects/probplots/dlbdss binom-pmf --n 10 --p 0.3 --k 4

# Binomial range: P(3 ≤ X ≤ 7)
/home/zk/projects/probplots/dlbdss binom-cdf --n 10 --p 0.3 --kmin 3 --kmax 7

# Poisson: P(X ≤ 2) when λ=3.5
/home/zk/projects/probplots/dlbdss pois-cdf --lam 3.5 --k 2

# Exponential CDF at x=5 with λ=0.4
/home/zk/projects/probplots/dlbdss exp-cdf --x 5 --lam 0.4

# Geometric pmf (k failures before 1st success), p=0.3, k=2
/home/zk/projects/probplots/dlbdss geom-pmf --p 0.3 --k 2

# Inequalities (bounds)
/home/zk/projects/probplots/dlbdss markov --mean 40 --t 240
/home/zk/projects/probplots/dlbdss chebyshev --sigma 2.1 --t 3

# CLT: P(95 < X̄ < 105) for μ=100, σ=15, n=36
/home/zk/projects/probplots/dlbdss clt --mu 100 --sigma 15 --n 36 --lower 95 --upper 105

Python API — Joint Distributions (Discrete)

import sys
sys.path.insert(0, "/home/zk/projects/probplots")
from stats_helper import compute_joint_stats

# 2×2 example (sums to 1.0):
joint = {(0,0):0.1, (0,1):0.2, (1,0):0.3, (1,1):0.4}
out = compute_joint_stats(joint)
print(out["marginal_X"])  # {0: 0.3, 1: 0.7}
print(out["marginal_Y"])  # {0: 0.4, 1: 0.6}
print(out["independent"]) # False
print(out["Cov"], out["Corr"])

Keys in result: support_X, support_Y, joint, marginal_X, marginal_Y, independent, E, Var, Cov, Corr.

FX‑991EX Cross‑Check (Exam Habit)

Build marginals: sum rows/columns.
Check independence by comparing f_{X,Y}(x,y) vs f_X(x)f_Y(y) for each cell.
Verify E[X] = Σ_x x f_X(x), E[Y] = Σ_y y f_Y(y); Cov = E[XY] - E[X]E[Y].

Plots (headless‑friendly)

If you’re on SSH, pass --out to save PNGs.

/home/zk/projects/probplots/dlbdss plot-pdf --dist normal --mu 0 --sigma 1   --out /home/zk/projects/probplots/stdnormal.png

/home/zk/projects/probplots/dlbdss sim-hist --dist normal --n 50000 --mu 0 --sigma 1   --bins 60 --out /home/zk/projects/probplots/sim_norm.png

/home/zk/projects/probplots/dlbdss sim-hist --dist binom --n 50000 --N 20 --p 0.3   --out /home/zk/projects/probplots/sim_binom.png

/home/zk/projects/probplots/dlbdss sim-hist --dist poisson --n 50000 --lam 3   --out /home/zk/projects/probplots/sim_pois.png

probplots‑web (Thin UI) — Plan

A separate repo will host a FastAPI backend + Tailwind UI on 127.0.0.1:5009, proxied at https://probplots.piapps.dev.
v2 adds /api/joint?pairs=... endpoint that calls stats_helper.compute_joint_stats(...).
See plan.v2.md for full build steps.

Performance Notes (Pi 5)

Closed‑form queries are ms‑level; tiny RAM.
Simulation memory ≈ 8 bytes × n for float64 (half for float32).
Headless plotting is automatic when no DISPLAY.
Keep the box responsive:
```
export OPENBLAS_NUM_THREADS=1
```

Changelog

v0.3 — Added stats_helper/JointDist and compute_joint_stats(...); updated docs.
v0.2 — Headless plotting, float32 option for simulations, project‑local launcher
v0.1 — Core distributions, inequalities, CLT, basic plots/sims

License

MIT (placeholder).

probplots — DLBDSS01-01 Statistics Helper (CLI + Plots)

Course-aligned command‑line tools for Probability & Descriptive Statistics (DLBDSS01‑01).
Runs great on Ubuntu and Raspberry Pi 5. Includes closed‑form distribution queries, inequalities/CLT helpers, simulations, and headless plotting for remote SSH sessions.

Main entry: /home/zk/projects/probplots/dlbdss
No need to activate the venv; the shebang points to the project’s Python.

Features

Probability basics: factorial, perm, comb
Distributions (PMF/CDF/quantiles): Binomial, Poisson, Geometric, Normal, Exponential, Uniform
Inequalities & theorems: Markov, Chebyshev, CLT (sample‑mean probability on an interval)
Simulations with visual overlays: sim-hist (Normal, Binomial, Poisson)
Headless plots via --out file.png (automatic Agg backend when no DISPLAY)
Pi‑friendly: optional --dtype float32 to halve RAM in large Normal simulations

Project Layout

/home/zk/projects/probplots
├── .venv/                # project virtualenv (created once)
├── bin/
│   └── dlbdss            # CLI entry point (shebang -> .venv/python)
├── dlbdss                # convenience launcher (execs bin/dlbdss)
└── README.md             # this file

Requirements

Python 3.10+ (tested with 3.13 on aarch64)
Packages: numpy, scipy, matplotlib (prebuilt wheels on Ubuntu/PI aarch64)

Install (one‑time)

# Create project
/usr/bin/mkdir -p /home/zk/projects/probplots/bin

# Virtualenv
/usr/bin/python3 -m venv /home/zk/projects/probplots/.venv
source /home/zk/projects/probplots/.venv/bin/activate

# Fast wheel installs
/home/zk/projects/probplots/.venv/bin/pip install --upgrade pip
/home/zk/projects/probplots/.venv/bin/pip install --only-binary=:all: numpy scipy matplotlib

Add the CLI script to /home/zk/projects/probplots/bin/dlbdss (already present in this setup).

For a project‑local launcher, dlbdss exists at the project root and simply execs bin/dlbdss.

Usage Cheat‑Sheet

Quick numeric queries

# Normal CDF: P(X ≤ 1.96) for N(0,1)
/home/zk/projects/probplots/dlbdss norm-cdf --x 1.96 --mu 0 --sigma 1

# Binomial: P(X = 4) for X~Bin(n=10,p=0.3)
/home/zk/projects/probplots/dlbdss binom-pmf --n 10 --p 0.3 --k 4

# Binomial range: P(3 ≤ X ≤ 7)
/home/zk/projects/probplots/dlbdss binom-cdf --n 10 --p 0.3 --kmin 3 --kmax 7

# Poisson: P(X ≤ 2) when λ=3.5
/home/zk/projects/probplots/dlbdss pois-cdf --lam 3.5 --k 2

# Exponential CDF at x=5 with λ=0.4
/home/zk/projects/probplots/dlbdss exp-cdf --x 5 --lam 0.4

# Geometric pmf (k failures before 1st success), p=0.3, k=2
/home/zk/projects/probplots/dlbdss geom-pmf --p 0.3 --k 2

# Inequalities (bounds)
/home/zk/projects/probplots/dlbdss markov --mean 40 --t 240
/home/zk/projects/probplots/dlbdss chebyshev --sigma 2.1 --t 3

# CLT: P(95 < X̄ < 105) for μ=100, σ=15, n=36
/home/zk/projects/probplots/dlbdss clt --mu 100 --sigma 15 --n 36 --lower 95 --upper 105

Plots (headless‑friendly)

If you’re on SSH, pass --out to save PNGs.

# Standard normal PDF → PNG
/home/zk/projects/probplots/dlbdss plot-pdf --dist normal --mu 0 --sigma 1 \
  --out /home/zk/projects/probplots/stdnormal.png

# Simulate Normal and overlay theory
/home/zk/projects/probplots/dlbdss sim-hist --dist normal --n 50000 --mu 0 --sigma 1 \
  --bins 60 --out /home/zk/projects/probplots/sim_norm.png

# Lighter RAM for very large n (float32)
/home/zk/projects/probplots/dlbdss sim-hist --dist normal --n 2000000 --mu 0 --sigma 1 \
  --dtype float32 --bins 80 --out /home/zk/projects/probplots/sim_norm_big.png

# Binomial and Poisson sims
/home/zk/projects/probplots/dlbdss sim-hist --dist binom --n 50000 --N 20 --p 0.3 \
  --out /home/zk/projects/probplots/sim_binom.png

/home/zk/projects/probplots/dlbdss sim-hist --dist poisson --n 50000 --lam 3 \
  --out /home/zk/projects/probplots/sim_pois.png

Help

/home/zk/projects/probplots/dlbdss --help
/home/zk/projects/probplots/dlbdss norm-cdf --help
/home/zk/projects/probplots/dlbdss sim-hist --help

FX‑991EX Cross‑Check (Exam Habit)

DIST → NORM/CD/INV for norm-cdf, norm-inv verification
BINM / POIS for binomial/poisson checks
CLT queries operate on the sample mean (X̄) with SE = σ/√n

Performance Notes (Pi 5)

Closed‑form queries are millisecond‑level, tiny RAM.
Simulation memory ≈ 8 bytes × n for float64 (half for float32).
Examples: n=1e5 → ~0.8 MB, n=1e6 → ~8 MB, n=1e7 → ~80 MB.
Headless plotting is automatic when no DISPLAY.
Keep the box responsive:
```
export OPENBLAS_NUM_THREADS=1
```

Roadmap

table-expect — E[X], Var(X) from value/probability lists
joint — marginalization + independence check from a joint table
--save-csv — dump simulation samples to a CSV
Add Beta/Gamma if they appear in course exercises

Changelog

v0.2 — Headless plotting, float32 option for simulations, project‑local launcher
v0.1 — Core distributions, inequalities, CLT, basic plots/sims

License

MIT (placeholder).

Acknowledgments

Built for DLBDSS01‑01 study workflow. Plots & sims inspired by the “simulate‑and‑compare” approach for intuition building.

Name		Name	Last commit message	Last commit date
Latest commit History 1 Commit
bin		bin
stats_helper		stats_helper
.gitignore		.gitignore
README.md		README.md
dlbdss		dlbdss
plan.md		plan.md
probplots.piapps.dev.nginx.md		probplots.piapps.dev.nginx.md

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probplots — DLBDSS01-01 Statistics Helper (CLI + Plots + Joint API)

Features

Project Layout

Install (one‑time)

Usage Cheat‑Sheet (CLI)

Python API — Joint Distributions (Discrete)

FX‑991EX Cross‑Check (Exam Habit)

Plots (headless‑friendly)

probplots‑web (Thin UI) — Plan

Performance Notes (Pi 5)

Changelog

License

probplots — DLBDSS01-01 Statistics Helper (CLI + Plots)

Features

Project Layout

Requirements

Install (one‑time)

Usage Cheat‑Sheet

Quick numeric queries

Plots (headless‑friendly)

Help

FX‑991EX Cross‑Check (Exam Habit)

Performance Notes (Pi 5)

Roadmap

Changelog

License

Acknowledgments

About

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Contributors 1

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probplots — DLBDSS01-01 Statistics Helper (CLI + Plots + Joint API)

Features

Project Layout

Install (one‑time)

Usage Cheat‑Sheet (CLI)

Python API — Joint Distributions (Discrete)

FX‑991EX Cross‑Check (Exam Habit)

Plots (headless‑friendly)

probplots‑web (Thin UI) — Plan

Performance Notes (Pi 5)

Changelog

License

probplots — DLBDSS01-01 Statistics Helper (CLI + Plots)

Features

Project Layout

Requirements

Install (one‑time)

Usage Cheat‑Sheet

Quick numeric queries

Plots (headless‑friendly)

Help

FX‑991EX Cross‑Check (Exam Habit)

Performance Notes (Pi 5)

Roadmap

Changelog

License

Acknowledgments

About

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