dsh-probstat

Deterministic probability & statistical-inference math for DeepSeek Harness (dsh). Four zero-runtime-dependency tools that replace the math agents get wrong most often: hallucinated z-table values, distribution cdf/quantile errors, wrong critical values, and sloppy compound-event identities.

中文简介：DeepSeek Harness 概率与统计推断数学工具箱——分布计算（正态/二项/泊松/指数/均匀/几何的 pdf/cdf/生存函数/分位数/统计量）、标准正态 z 表换算、置信区间（均值 z/t + 比例 Wilson）、事件概率恒等式（并/交/条件/贝叶斯）。零运行时依赖，纯确定性计算。

Install

dsh plugin --profile web add github:TYEclipse/dsh-probstat

Tools

Tool	What it does
dist_calc	pdf / cdf / survival / quantile / stats for 6 distributions
z_score	standard-normal table math (z ↔ probability)
confidence_interval	mean intervals (z or t) and Wilson proportion intervals
event_probability	union / intersection / conditional / Bayes / complement / at-least-one

dist_calc

Distributions: normal (mean, sd — default standard normal), binomial (n, p), poisson (lambda), exponential (rate lambda), uniform (a, b), geometric (p). Operations: pdf, cdf (P(X ≤ x)), survival (P(X > x)), quantile (inverse cdf at probability q), stats (mean / variance / sd).

Examples:

• distribution: "normal", x: 1.96 → cdf 0.9750022 (P(Z ≤ 1.96))
• distribution: "binomial", operation: "quantile", n: 10, p: 0.5, q: 0.95 → 8
• distribution: "poisson", operation: "survival", lambda: 3, x: 5 → 0.08391794
• distribution: "geometric", operation: "stats", p: 0.5 → mean 1, variance 2

Conventions: the geometric distribution counts failures before the first success (support k ≥ 0, P(X = k) = p·(1−p)^k). Quantiles of discrete distributions return the smallest k with P(X ≤ k) ≥ q.

z_score

Modes: to_prob (z → probability + percentile), from_prob (probability → z), two_sided (z → two-tailed p-value), between (z1, z2 → probability between; order is sorted internally).

• mode: "between", z1: -1.96, z2: 1.96 → 0.9500043
• mode: "two_sided", z: 2.5 → p-value 0.01241936

confidence_interval

Kinds: mean_z (population mean, known sigma), mean_t (population mean, unknown sigma; Student-t with df = n − 1), proportion (Wilson score interval — stays valid for small samples and extreme proportions, unlike the naive Wald interval). Default confidence level 0.95.

• kind: "mean_t", mean: 72.5, sd: 8.2, n: 25 → [69.115, 75.885] (t* = 2.0639, df = 24)
• kind: "proportion", successes: 40, n: 100 → [0.30940, 0.49800]
• kind: "proportion", successes: 0, n: 50 → [0, 0.07135]

event_probability

Operations: union (P(A or B); independent default true, false treats events as mutually exclusive), intersection (independent events), conditional (P(A|B) = P(A and B)/P(B)), bayes (posterior from prior, true-positive and false-positive rates), complement, at_least_one (1 − (1−p)^n).

• operation: "bayes", prior: 0.001, truePositive: 0.99, falsePositive: 0.01 → 0.09016
• operation: "at_least_one", p: 0.05, n: 20 → 0.64151

Numerics & precision

• Normal cdf: Abramowitz & Stegun 7.1.26 erf fit, absolute error ≤ 1.5e-7 (far beyond published 4-decimal z-tables).
• Normal quantile: Acklam inverse normal, relative error < 1.15e-9.
• Binomial / Poisson: exact pmf via recurrence and cdf by summation (no combinatorics overflow); quantiles by monotone search.
• Student-t: regularized incomplete beta (Lentz continued fraction) + Lanczos log-gamma; cross-checked against published t-table values (2.2281, 2.0452, 1.8125, 1.984).
• Exponential / uniform / geometric: closed forms.
• All validation errors return valid: false with an explanatory error string; no tool ever throws on bad numeric input.

Development

pnpm install
pnpm build
pnpm test   # 37 tests; anchors from test/anchors-probstat.py (independent Python oracle)
pnpm lint

License

MIT