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AIwinter

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AIwinter
Sep 29th, 2024
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  1. import numpy as np
  2. import random
  3. import math
  4. import pandas as pd
  5.  
  6. alpha = 0.05
  7. from google.colab import drive
  8. drive.mount('/content/drive')
  9. file_path = '/content/drive/MyDrive/table.txt'
  10.  
  11. a = float(input('Введите параметр сдвига(a): '))
  12. lambdaP = float(input('Введите параметр масштаба(лямбда): '))
  13. N = int(input('Введите объём выборки: '))
  14.  
  15. "вывод: Введите параметр сдвига(a): -1
  16. Введите параметр масштаба(лямбда): 1
  17. Введите объём выборки: 1000"
  18.  
  19. def distributionFunction (x):
  20. return math.atan((x - a) / lambdaP) / math.pi + 0.5
  21.  
  22. R = np.zeros(N)
  23. for i in range (0, N):
  24. R[i] = a + lambdaP * math.tan(math.pi * (random.random() - 0.5))
  25. RSorted = R.copy()
  26. RSorted.sort()
  27. RSorted = np.asarray(RSorted, dtype=float)
  28. np.set_printoptions(formatter={'float': '{:f}'.format})
  29. print(RSorted)
  30. print(R)
  31.  
  32. "вывод: [-79.854081 -60.276525 -42.441431 -38.149847 -36.979664 -31.878634
  33. -27.867284 -27.533557 -26.159700 -21.429084 -20.216917 -20.102235
  34. -20.076769 -19.674909 -19.590602 -19.125453 -18.462549 -18.399320
  35. -17.707582 -15.798814 -15.292545 -15.051831 -14.796829 -14.737687
  36. -14.715679 -12.178563 -11.757177 -11.729978 -11.611236 -11.249558
  37. -10.827199 -10.771752 -10.542624 -10.302350 -10.193830 -10.183896
  38. -10.129909 -10.081322 -10.066013 -9.422192 -9.207905 -8.664409 -8.393499
  39. -8.391323 -8.388748 -8.381779 -8.361344 -8.356368 -7.820638 -7.509389
  40. -7.317908 -7.220271 -7.214352 -7.098820 -6.947402 -6.927981 -6.661438
  41. -6.628479 -6.565127 -6.431360 -6.395277 -6.315531 -6.310739 -6.261490
  42. -6.192714 -6.041403 -5.970423 -5.936931 -5.883594 -5.726180 -5.682571
  43. -5.624340 -5.502221 -5.456204 -5.335302 -5.297016 -5.284165 -5.056535
  44. -4.943126 -4.894715 -4.888954 -4.882085 -4.840192 -4.750295 -4.708182
  45. -4.637710 -4.563989 -4.557379 -4.538786 -4.471553 -4.449312 -4.438574
  46. -4.434896 -4.421976 -4.387669 -4.342015 -4.330346 -4.324358 -4.299042
  47. -4.291158 -4.265365 -4.192583 -4.187468 -4.170293 -4.147321 -4.087805
  48. -4.064614 -3.975058 -3.869503 -3.831138 -3.818295 -3.817715 -3.760899
  49. -3.745323 -3.696766 -3.692203 -3.686412 -3.665732 -3.643854 -3.507630
  50. -3.503315 -3.498043 -3.466472 -3.464697 -3.453765 -3.449819 -3.447580
  51. -3.425944 -3.370819 -3.365554 -3.343168 -3.336270 -3.289733 -3.281028
  52. -3.279131 -3.271646 -3.220992 -3.213519 -3.204496 -3.201276 -3.194162
  53. -3.186588 -3.148611 -3.145226 -3.145226 -3.124087 -3.108521 -3.090821
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  206. 12.499334 -0.454357 -5.883594 0.490433 -1.420212 7.159985 -2.786707
  207. -3.745323 -2.270843 2.214618 -1.206363 -19.674909 -1.570398 11.751516
  208. -31.878634 -0.717651 -0.156518 1.126484 -1.375244 -3.336270 -10.542624
  209. -1.114742 -0.914904 -14.796829 1.773778 -0.610355 1.510019 -1.701066
  210. 2.377081 -0.552154 1.837537 0.338950 -2.214430 -1.959871 -4.894715
  211. -8.391323 -1.589370 -1.796564 -2.305636 -1.926440 -1.069030 -1.605745
  212. -1.625226 -1.482491 -0.764809 -1.891019 -3.692203 -10.066013 0.827120
  213. -1.785082 1.330078 -0.409990 -2.772438 -5.297016 0.042918 6.567557
  214. -1.075710 -1.734431 -1.606122 -1.137398 -0.593040 -6.261490 5.645703
  215. 9.800134 -8.664409 2.315756 -0.580125 -1.015750 -2.358708 0.218904
  216. 3.972167 -0.662156 3.525644 -0.690088 -1.179454 -0.508328 -2.795824
  217. -20.102235 -1.259381 -1.277824 -1.893963 -0.916896 -0.602827 2.529546
  218. -0.922503 -1.605057 -1.214364 -1.613436 1.461655 -0.949510 2.374423
  219. -1.147601 1.026385 -0.488208 -21.429084 -3.686412 -1.547266 -2.243032
  220. -0.636501 0.765021 -1.523289 1.458856 -2.873575 -3.034402 -2.010267
  221. -2.132361 -2.965910 -6.192714 -3.108521 -0.731589 1.106446 -2.565783
  222. -1.671534 -0.791487 1.483653 4.263428 -1.250391 -1.222394 -14.715679
  223. -6.431360 -1.251263 -0.687010 1.163871 -0.107827 -2.581005 -2.285000
  224. 0.302350 -3.817715 -2.529774 -0.168662 0.581800 -2.838389 8.022871
  225. 2.478271 -1.330984 0.491306 -0.948612 0.250348 -1.462890 0.492369
  226. -2.467941 -1.591797 0.519590 -1.014484 -1.724905 -1.863108 -1.344870
  227. -0.994783 -1.498516 -0.189614 13.219293 -1.571999 -0.776734 578.250967
  228. -3.464697 -0.555179 -1.374316 -17.707582 -1.178957 -0.531081 -0.815730
  229. -0.182756 6.354766 -3.365554 -0.263474 0.257674 2.028347 0.358267
  230. -1.775228 -0.127966 2.059994 0.827786 -1.864172 -1.761392 4.318293
  231. 16.886928 -10.827199 -0.270141 -2.300475 -1.102850 -4.324358 -0.793394
  232. 1.055861 -4.471553 3.009483 -1.364185 -1.607002 -3.281028 -0.120213
  233. -2.304271 -3.145226 0.242020 -0.948396 21.416550 -0.297102 -0.982561
  234. -2.596697 -0.828447 -3.831138 0.133178 1.797586 -1.482332 -2.605295
  235. -0.923319 -0.489676 -12.178563 -1.789932 0.257039 -5.502221 -0.373216
  236. -1.236540 -2.314635 -1.784392 -0.752310 -1.941429 -0.735845 -2.713151
  237. -1.511748 -0.589941 -0.813219 -0.258747 -0.591860 -2.577537 -2.187116
  238. -4.888954 12.270335 0.780319 -1.363873 -3.643854 -0.640249 -3.194162
  239. -0.207043 -10.302350 -0.838037 -8.393499 -0.215330 -0.977115 1.160776
  240. -0.570312 -1.196358 -0.746020 -1.478860 -0.783659 0.040238 -3.289733
  241. 0.160661 -2.508460 -2.789449 -2.471363 -2.889682 0.114759 -0.024645
  242. -1.932572 -3.453765 -0.692058 2.596467 -2.696718 -0.244929 -2.240718
  243. -0.419961 -2.279928 -1.062630 -0.364430 -0.564639 -1.595760 -3.204496
  244. -0.863720 -1.531774 1.731570 2.080456 1.112166 9.389906 -1.835500
  245. -0.297335 -0.847154 -0.999242 -2.697328 -0.836246 -0.032039 -1.780129
  246. -0.892729 -1.189371 1.801938 -0.837147 -3.975058 6.726048 1.775091
  247. -2.732071 -0.802016 -0.770109 -0.336181 -1.011218 16.847719 -2.276514
  248. -1.054168 -0.440069 -2.949859 0.397221 6.327168 -0.284948 -0.947573
  249. -3.343168 -0.372844 -2.593478 -1.634542 -0.122098 -2.849868 -1.874603
  250. -6.395277 -0.260184 -2.179862 -2.586041 0.083736 1.715989 -6.310739
  251. 13.158322 -1.060615 -3.213519 -1.870130 2.877820 0.200070 10.989399
  252. -1.416402 -1.859213 0.411200 -4.538786 -1.538328 -0.854661 4.278270
  253. -0.864966 -0.349198 -4.299042 -1.085123 -1.594019 -2.041206 -0.745660
  254. -0.287836 -1.050727 -1.872019 -2.433190 -1.819578 -1.989833 -3.503315
  255. -10.193830 -2.165502 -1.928161 0.280780 0.141256 -3.425944 -0.345515
  256. -0.921919 -1.667389 -0.470464 -0.963251 -1.802874 -5.726180 -10.183896
  257. -1.723726 -2.862638 -0.492091 -1.655848 5.869067 -0.931777 -1.118718
  258. -20.216917 -0.968217 -0.485748 -1.402719 -1.301967 -0.889755 -11.757177
  259. -1.407042 1.130872 -1.649531 -1.618238 0.539862 -0.561428 -1.327816
  260. -1.815004 -1.936345 -1.725402 -4.637710 -2.094163 -1.860475 -4.291158
  261. -1.143441 -2.066946 -1.180341 -1.697654 -3.665732 -3.271646 -2.307312
  262. -0.703899 -1.032441 -0.654502 0.794277 -0.933871 1.811493 4.440897
  263. -8.388748 -2.404199 -2.453215 0.140106 -4.192583 -27.533557 -79.854081
  264. -0.459362 -1.556513 -0.863383 -0.057235 -8.356368 -2.628141 -0.977121
  265. -1.064050 0.843669 0.663469 -0.684618 -0.514257 0.723191 -1.152594
  266. -15.051831 -1.541981 3.909402 -0.192459 -1.590874 -1.348877 -4.449312
  267. -0.958054 -2.026363 -2.858951 3.959543 -0.582986 -0.346873 0.149885
  268. 0.066250 -1.198095 -4.087805 2.844932 -0.670199 -7.214352 -0.439674
  269. 0.888495 -0.105269 -1.487603 1.172657 0.348555 8.223151 1.699483
  270. -36.979664 -0.679649 -6.041403 -1.353516 -1.416828 -1.506061 -1.468272
  271. 0.146782 -15.798814 -0.694408 -5.682571 -0.677263 -38.149847 -2.267123
  272. -2.315615 -2.018353 1.587279 -11.611236 -4.387669 -3.760899 1.778233
  273. 2.093690 4.054337 -1.604565 -0.075050 0.202986 -1.271660 -1.206832
  274. -0.579305 -0.298612 13.183630 -10.771752 -2.420556 1.801806 -1.268058
  275. -3.869503 0.405236 -1.456464 0.166431 -2.126541 0.513136 1.992124
  276. 1.767963 -0.823481 -1.325412 -0.295530 0.736359 -0.906295 -0.571622
  277. -11.249558 -18.462549 -1.048672 -0.603903 -7.220271 -0.593039 -3.507630
  278. 0.303792 -4.563989 -1.098146 -19.590602 1.602100 8.864719 -0.987629
  279. 7.923705 -1.002583 -0.849641 -1.856667 -4.170293 -1.758109 -1.694980
  280. -1.541943 -0.919788 0.269143 -0.574314 -2.182820 -4.750295 -1.990460
  281. -1.133759 -2.083077 -1.352781 -1.347878 -1.181337 0.030663 -0.551084
  282. -1.178131 -0.682649 -1.402780 -27.867284 -1.297461 3.515835 -1.319419
  283. -1.787095 -1.072922 9.604152 -1.543485 -0.743754 -2.572602 -1.061126
  284. 5.351533 -0.896838 -5.970423 2.962963 -0.985366 -3.186588 -0.435668
  285. -0.617511 -0.634905 -2.524923 0.426912 -0.593014 -2.093131 -0.888736
  286. -1.361475 0.375293 -1.306019 -2.651619 2.951166 -1.070875 0.707684
  287. 4.444854 -2.788224 -6.661438 -2.248533 3.821652 2.311494 -0.535057
  288. 1.671197 0.873669 -0.463001 -0.723134 -0.920727 -4.330346 -3.040967
  289. -9.422192 -0.367329 3.641221 -3.124087 -6.565127 -1.097776 -1.510389
  290. -2.581358 -1.731329 -1.210763 -0.475804 5.074808 -9.207905 -0.892946
  291. -2.623123 0.528934 -6.927981 -2.580664 -1.953729 -1.311564 4.069000
  292. -2.011265 -3.148611 -4.342015 -0.584469 1.113488 -1.811968 -2.021518
  293. 2.222890 -1.428866 -2.469188 -0.014609 -0.932230 -0.850597 -1.357058
  294. 1.764687 -0.658760 1.041736 -1.001062 -1.201229 -1.029201 -0.948220
  295. -1.036643 -1.059872 -1.139351 293.762337 -1.966415 -2.044168 -0.238473
  296. -3.039144 -1.069334 -2.213462 -1.101070 -2.854437 0.272323 -10.081322
  297. -0.284614 -0.330423 -2.025020 -0.853170 -2.318835 -8.361344 0.318734
  298. -5.936931 -1.609015 -0.857069 -2.814996 -1.135620 -0.880280 -0.762880
  299. -2.125828 -0.574988 0.498033 -1.728332 1.831007 -0.772046 1.887910
  300. -2.833914 9.675829 -4.064614 -0.800809 -0.807329 5.901551 -1.955318
  301. -1.850944 14.902898 -0.097423 -1.808393 -0.413084 -5.056535 -1.928426
  302. -0.866776 -0.960754 -1.751910 -11.729978 1.540543 -7.820638 -0.926353
  303. -1.595418 -0.876714 -3.447580 -1.867714 -1.523818 -1.797754 -0.683191
  304. -1.774566 0.764872 -2.641176 -2.485142 -0.587673 -1.144596 -2.437195
  305. 0.997263 -4.265365 -1.813409 -0.501619 0.427650 4.610259 -0.207465
  306. 0.052677 -0.338835 -1.196809 6.423232 -0.346848 -7.317908 -0.776530
  307. -2.768766 -0.491336 -1.702888 8.476714 -2.595218 -1.517390 -0.264290
  308. 7.668780 2.655263 -0.903835 -3.696766 -0.872663 -2.266285 -0.073118
  309. -2.611804 12.375031 -0.326010 -1.526479 -1.687338 -1.721619 -2.868880
  310. -1.688225 0.203255 1.306225 -0.223394 -0.257211 -3.466472 0.519822
  311. -0.443319 -0.976827 -60.276525 -0.866929 -1.652113 28.071417 -1.296740
  312. -2.671570 -14.737687 4.093320 -4.882085 -0.653549 -1.006103 -1.457551
  313. -1.945036 -2.398681 -1.336318 -1.432247 -42.441431 -8.381779 -0.405758
  314. -0.122868 -1.723382 3.413704 -1.265584 -0.508216 -1.116591 -0.417388
  315. 1.356702 -4.840192 -2.564113 -4.147321 -0.975026 -1.761577]"
  316.  
  317. xiTable = pd.read_csv(file_path, sep="\t", header=None)
  318. print (xiTable)
  319. xiTable = np.asarray(xiTable, dtype=float)
  320.  
  321. "вывод: 0 1 2 3 4 5 6 7
  322. 0 0 0.95000 0.75000 0.25000 0.10000 0.05000 0.01000 0.00500
  323. 1 1 0.00393 0.10153 1.32330 2.70554 3.84146 6.63490 7.87944
  324. 2 2 0.10259 0.57536 2.77259 4.60517 5.99146 9.21034 10.59663
  325. 3 3 0.35185 1.21253 4.10834 6.25139 7.81473 11.34487 12.83816
  326. 4 4 0.71072 1.92256 5.38527 7.77944 9.48773 13.27670 14.86026
  327. 5 5 1.14548 2.67460 6.62568 9.23636 11.07050 15.08627 16.74960
  328. 6 6 1.63538 3.45460 7.84080 10.64464 12.59159 16.81189 18.54758
  329. 7 7 2.16735 4.25485 9.03715 12.01704 14.06714 18.47531 20.27774
  330. 8 8 2.73264 5.07064 10.21885 13.36157 15.50731 20.09024 21.95495
  331. 9 9 3.32511 5.89883 11.38875 14.68366 16.91898 21.66599 23.58935
  332. 10 10 3.94030 6.73720 12.54886 15.98718 18.30704 23.20925 25.18818
  333. 11 15 7.26094 11.03654 18.24509 22.30713 24.99579 30.57791 32.80132
  334. 12 20 10.85081 15.45177 23.82769 28.41198 31.41043 37.56623 39.99685
  335. 13 25 14.61141 19.93934 29.33885 34.38159 37.65248 44.31410 46.92789
  336. 14 30 18.49266 24.47761 34.79974 40.25602 43.77297 46.97924 50.89218"
  337.  
  338. def findTableXi(k, alpha):
  339. column = 0
  340. for i in range (1, xiTable.shape[1]):
  341. if xiTable[0][i] == alpha:
  342. column = i
  343. if column == 0:
  344. return 'Нет нужного значения альфа в таблице'
  345. i = 1
  346. while i < len(xiTable) - 1 and xiTable[i][0] < k:
  347. i += 1
  348. if k == xiTable[i][0]:
  349. xi = xiTable[i][column]
  350. elif k > xiTable[len(xiTable) - 1][0]:
  351. xi = xiTable[len(xiTable) - 1][column] + (xiTable[len(xiTable) - 1][column] - xiTable[len(xiTable) - 2][column]) / (xiTable[len(xiTable) - 1][0] - xiTable[len(xiTable) - 2][0]) * (k - xiTable[len(xiTable) - 1][0])
  352. else:
  353. xi = xiTable[i - 1][column] + (xiTable[i][column] - xiTable[i - 1][column]) / (xiTable[i][0] - xiTable[i - 1][0]) * (k - xiTable[i - 1][0])
  354. return xi
  355.  
  356. intervalsNumber = int(1 + 3.322 * math.log10(N))
  357. k = intervalsNumber - 1
  358. XSquaredE = 0
  359. j = 0
  360. for i in range (0, intervalsNumber):
  361. n = 0
  362. while j < N and RSorted[j] < RSorted[0] + (RSorted[N - 1] - RSorted[0]) * (i + 1) / intervalsNumber:
  363. j += 1
  364. n += 1
  365. XSquaredE += (n - N * (distributionFunction(RSorted[0] + (RSorted[N - 1] - RSorted[0]) * (i + 1) / intervalsNumber) - distributionFunction(RSorted[0] + (RSorted[N - 1] - RSorted[0]) * i / intervalsNumber))) * (n - N * (distributionFunction(RSorted[0] + (RSorted[N - 1] - RSorted[0]) * (i + 1) / intervalsNumber) - distributionFunction(RSorted[0] + (RSorted[N - 1] - RSorted[0]) * i / intervalsNumber))) / (N * (distributionFunction(RSorted[0] + (RSorted[N - 1] - RSorted[0]) * (i + 1) / intervalsNumber) - distributionFunction(RSorted[0] + (RSorted[N - 1] - RSorted[0]) * i / intervalsNumber)))
  366.  
  367.  
  368. XSquaredT = findTableXi(k, alpha)
  369. print('Теоретическое значение хи-квадрат: ' + str(XSquaredT))
  370. print('Расчётное значение хи-квадрат: ' + str(XSquaredE))
  371.  
  372. "вывод: Теоретическое значение хи-квадрат: 16.91898
  373. Расчётное значение хи-квадрат: 5.53163152806912"
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