GB T 4086.3-1983 统计分布数值表 t分布.pdf

1、中华人民共和国国家标准UDC 311.13(083.Sl 统计分布数值表t分布GB 4086.3-83 Tables for statistical distributions t-distribution 斗标准包恬Jr:11学rji常用的t分布的两种数值表，它们的名称、表距和精度如f,I沙市的数灰V二l( l )20( 2 )30( 5 )50, 60 6 （.小数I分布分f!r.数表t二。（0.1)4 (0.2)5(0.5)7 户0. 5 ( 0. 05) 0. 95，。.975,0.98, 0.99, 0.995, 0.9975, 0.998, 0.999, 0.9995, 0.999

2、8,0.9999 V= j ( j )30( 2 )40( 5 )70(10)120, 150, 180, 240, OG 巾的分位数对应子i-:flJ!lj慨来。虫然灰1j1 台山56位小数，但是在使用中需要取几价，要山实际问题决定。在应用中不能满足妻求时，口I参考附录的处理方法。5位小数国家标准局198312 21发布1984 10 01实施l 2也GB 4086. 3-83 P (I , v ) dt t分布函数表r i!c, 0.99:i211 0.993571 hv2778 1E41ny 3D61句己7J80499?09 9000? 0060U 。？手61570.916910 0.9

3、97519 0.998009 0.918404 0.995973 0.99674自0.997376 日.997885 0.998296 0.995760 0.996560 0.997211 0.997740 0.998170 0.99551句口.9963410.997018 0.997571 0.998021 0.995224 0.996口840.996790 0. 997369 0.997844 0.994881 0.995777 0.996516 0.997126 0.997629 0.994467 0.995405 0.996184 0.996830 0.997365 0.993960

4、0.994948 0.995773 0.996461 0.997035 3.0 3. 1 3.2 3.3 3.4 2610AC 7COY-5巳245巳ooun04oe9 vnynyfyF DCCUO 0 991802 0.9906 0. 99921,0 0. 91 315 0.999519 。.998722 0.998976 0 990181 0.999344 0.999t,75 0.998628 0.998896 0.999111 0.999285 0.999424 0.998518 0.998800 0.999029 0.999214 0.999363 0.998388 0.998687

5、0.998930 0.999128 0.999289 0.998232 0.998551 0.998811 0.999025 0.999199 0.998043 0.998384 0.998665 0.998896 0.999087 0.997809 0.998177 0.998482 0.998735 0.998945 55982 11426 5?257 77888 9999? 9779P OODOO 3.5 3.6 3.7 3.8 3. 9 0. 9i6!, 097（，口。，QO（）二日，？9150.99994飞776、吕1$403 670099 00909 3?099 99907 000

6、00 0.999580 0.999731 0.999827 0.999889 0.999128 0.999536 0.999699 0.999804 0.999872 0.999917 。.999484 0.999661 0.999776 0.999852 0.999902 0.999420 0.999614 0.999742 0.999827 0.999883 0.999342 0.999555 0.999698 0.999794 0.919859 刚刚刚刚附。.9991190.999384 0.999567 0.999695 0.999783 0.998957 0.999257 0.999

7、68 0.999618 0.999723 4. 0 4.2 4.4 4.6 4. 8 onjhJ7U J381VPG OOU子。99990 。0197心90990 qODD- 0.999960 0.999987 0 009们960.999998 臼.999999口，9999540.999984 0.999994 0.999998 0.999999 0.999945 0.999980 0.999993 0.999997 0.999999 0.999935 0.999976 0.999991 0.999996 0.999999 0.999921 0.999969 0.999988 0.99999

8、5 0.999998 0.999903 0.999961 0.999984 0.999993 0.999997 0.999879 0.999949 0.999978 0.999990 0.999995 0.9998,5 0.999932 0.999969 0.999985 0.999993 。.9997990.999907 0.999955 0.999978 0. 999989 5.0 5 5 6.0 6. 5 7 .。1, I z P (I, v）二ldt J .VB (1/2, v/2) 0 I 22 24 26 28 30 35 40 eS 50 60 o.o 0.500000 0.50

9、0000 o.scccco o.scocco o.soccoo 0.500000 0.500000 o.scccoc 0.500000 0,; )0000 0. I 0.539375 0.539413 0.539444 0. 5394 72 0.53495 0.539543 0.539578 0.5396日60.559628白.539661.2 0.578341 0.578417 ：578482 0.578537 0.57 585 0.578681 0.578753 0.5788C9 0.)18854 口，578922.3 0.616503 0.6j660 .616719 。.61680z0.

10、61%877 0.617024 0.617135 0.617221 口.6172900.61739气0.4 0.653493 。.636 3 0.653788 0.65390 0.65日050.654206 0.654358 0.654475 0.654570 。654711 0. 5 0.618980 0.689186 0.689360 .689509 0.6868 0.689898 0.690093 0.690244 0.690366 0,690548 。0.72682 7229) 0.73150 .723334 0.72 4 0.723814 0.724055 0.724242 0.72

11、4392 0,724617 o. 0.7 4368 .7546 0.7 4928 .755149 0. 755 40 0.755723 0.756011 。7562350.756414 0. 756684 0.8 0.783868 0.784221 0. 784520 0. 784777 0.78000 。.785446 。787820.786043 。78622。.7865670, 9 0.811067 0.811469 。.8118100.812102 0.81 356 0.812864 0.81 247 0.813544 0.813830.814141 I . 0 0.835908 0.

12、8637 8!67 .837063 0.837346 0.837913 0.838339 0.838671 0.838937 0,839337 1. I o. sf saa 0.8 8 8 9 8965 0. 859960 0. 860580 0.861046 。.8614090.861700 。.8021371. 0.8i49 .8 07 0.8 9 0 .8 990 0.880235 0.8801CO 0.881401 。.8817900.882103 0.882072 1. 0.89 471 .897026 0.8 7496 0.897899 0.898250 0.898951 0.89

13、1479 0.899890 0.900219 0.900713 1. 4 0.912271 。.9128460.913333 0.913752 0.914115 0.914842 0.915389 0.915815 0.916156 0.91666吕1. 5 0.926085 ：665了7 0.97170 。00 927597 0.927967 。.9287090.929267 0.929701 。.93CC90.930571 1. 0.938069 0.9 9159 .93989 0.99961 0.94706 941266 0.941702 0.942050 0.942574 0.94？

14、2 0.948386 .9 9467 949 92 0.9 0261 0.95 999 .951552 0.951983 0.952328 0.952845 1. 8 0.957205 0.957778 958262 0.95867 0.959037 0.959757 0.960297 0.960717 0.961052 0.961556 1. 9 0.964690 0.965243 。.9657110.96611 0.966459 0.9占71520.967671 。.9680740.968396 0.968819 . 0 0.97102 0.97150 0.9)1976 972357 0.

15、972687 0. 973346 0. 973839 。.9742210.07452占0,97句9830.9762 1 0.9767 i 0.9 7209 .977568 0.977879 。.9784970.978959 2.3 0.980697 0.9811 0.981553 0.981887 0.98176 。.9827500.983177 2. 0.984346 0.9847 0.985136 i.9851;4 0.98 709 0.986236 0.986628 2.4 。.9873520.987745 0.988075 .988 5 0.988597 0.989075 0.9894

16、30 2.5 0.989816 0.990173 0.990471 0.990725 0.990942 。9913720.991690 Z.6 。.9918270.992148 0.992415 0.99264 0.992836 。.993219。.993501 7 。.9934610.99747 。.9于398 0.99418 0.99458 0.994696 。.994943.8 o.994782 o.99 of5 0.9 524 0。.995422 0.995 73 0.99569 。.9960842.9 0.995847 0.9960 0.9 6254 .996409 0.996540

17、 0.996 96 。.996982. 0 0.996701 0.9997 ：i 0.997191 。.9973050.997526 0.99768) 0.99738 0.997810 0.997908 0.998096 0.998232 3.2 0.997934 。.99800.998297 0.998381 。.9985410.998655 3. 3 o.98369 0. 99 。.9984 4 0.99199 0.99 596 0.998680 0.998750 0.99B8B5 0. 998981 3.4 。.98714 0.998821 。.9989080.998979 0.9990

18、38 3.5 0.998988 0.999262 0.99909 99152 0.999211 .6 i 0.999204 。.99921 .9 934j 0.9999 0.999434 .7 0.999375 0.999440 0.9949 0.999 3 0.999568 3.8 3.9 4.0 4.2 4.4 4. 6 4. 8 5.0 5.5 6.0 6.5 7. 。，9995090.999564 0.9 9607 0.999642 0.999670 0.999615 0.999661 。.9996970.999725 0.999749 .999698 。.9997z70.999766

19、 0.99979 0.999809 .999815 0.9998 1 0.999861 0.99987 0.999890 。，9998860.999904 0.999918 0.999929 。.999937 0.91993 日，9999430.999952 0.99999 。.9999640.99995 0.999965 0.999972 。.9991 6 口，9999800.999974 0.99999 0.9998 0.999986 0.999988 0.999992 0.9199 4 0.9 999 0.999996 0.999990.999998 0.9999 8 0.999999

20、0.999999 0.991919 0.99999。9 0.911199 1 000000 1 . 000000 1.00CCCO 1.0000 0 1.000000 1.000000 1.000000 1.01COCQ 在表-ir 11 HJI丘叫口I；出I分布函数尸（I g川的数俏。19, tJJv04s平nt3, Pll;V）工0.997811000.999151 0.999230 0.999356 0.999421 0.999512 0.999566 0.999632 。.999676。，999723。，9997580. 919792 0.999821 0.999844 0.99986

21、7 0.999913 0.919928 0.999952 0.999961 0.99997 0.911179 D.99998 0. 9问9890.999992 0.99194 0.999998 。.9999991.0COOOO 1 . 000000 1.CCCOCO 1 . 000000 1.00COCO 1.0CCOOO 0.979317 。.979600.980CC:9 0.983508 0.98377 0.98句1650.986930 0.98717 0.987529 0.989703 0.989920 0.990242 0.991934 。.992128。90241号0.993717

22、0.993888 0.9ic 14口0.995132 0.995281 0.995502 0.996249 。.9963780.99o5t7 。.9971240. 997231, 0.997396 0.997日050.99789; 0.998031 0.998333 0.99841 。.9985270.9987句。0.998806 。.9989010.999052 。.9991060 9!918) 0.999289 。.9993340.999398 0.999469 0.9995(6 0.999558 0.919605 自.999635 。9196770.911708 。.9997310.99

23、9765 。，999784。.9998030.9;9830 0.911841 0.999856 。斤99817。.9998830.91989) 0.99912 0.999938 。.999945。.99955。.9999610.9197己。99:。.999983。.99098;0 91198 0.999991 。.999990.9Y9995 。9999950.999996 口号0999;0.911999 0.999999 I O丁）QCGO1.CcCCOO I. 000000 1.0COOOO I ,OC CCO I. 000000 1 . I000001.0CCCCO 1.0CCCCO 1

24、 00000) GB 4086. 3-83 p 一dt p t分布分位数表( 1 + I 2） 、二vR(l 2,V 2) 川）J 2 v 、丁7B(/2, v/2! 川）:J二2（ v ) 0.9999 0.9998 。.999)0.9990 0.9980 。.9975。.9950。.99000.9800 。.9750 mmmm叩JmmuJ引丑mm引仍引弘02179 26053 557PP D4064 26446 89573 . 16433 3 15.89454 4.84873 3.48191 2.99853 2.75651 12.70620 4.30265 3. 18245 2.7764

25、5 2.57058 12345 93032 7句。843203 2641p o0406 . E7665 1.01392 6.31077 5.81128 5.46082 5.20224 5.95882 5.40788 5.04131 4.78091 4.58689 5.20763 4.78529 4.5口口794.29681 4.14370 32514 11952 47046 20931 52987 . 44333 4.31683 4.02934 3.83252 3.68966 3.58141 3.70743 3.49948 3.35539 3.24984 3. 16927 3. 14267 2

26、99795 2.89646 2.82144 2.76377 2.61224 2.51675 2.44898 2.39844 2.35931 2.44691 2.36462 2.30600 2.26216 2.22814 5.45276 5.26327 5. 11058 4.98501 t,. 88000 5.00400 4.84740 4.72069 4.61613 4.52842 4.43698 4.31779 4. 22083 4.14045 4.07277 4.02470 3.92963 3.85198 3.78739 3.73283 74713 75688 39874 24日3p65

27、443 . 33333 3.49661 3.42844 3.37247 3.32570 3.28604 3.10581 3.05454 3.01228 2.97684 2. 94671 2.71808 2.681(0 2.65031 2.62449 2.60248 2.32814 2.30272 2.28160 2.26378 2.24854 91795 98374 08041 07643 21111 . 22222 6789012345 111111 4.79091 4.71441 4.64801 4.58986 4.53852 4.45382 4.38962 4.33378 4.28479

28、 4.24147 4.01500 3.96513 3.92165 3.88341 3.84952 57801 17448 650?1 84175 66655 . 33333 3.35791 3.32590 3.29788 3.27315 3.25116 3.25199 3.22245 3.19657 3.17372 3.15340 2.92078 2.89823 2.87844 2.86093 2.84534 2.58349 2.56693 2.55238 2.53948 2.52798 65006 38776 53346 32109 22221 . 22222 2.11991 2.10982

29、 2.10092 2.09302 2.08596 6789却4.49286 4.45199 4.41520 4.38192 4.35165 80412 831?2 287日3020308 21110 . 44444 3.81928 3.79213 3.76763 3.74540 3.72514 3.52715 3.50499 3.48496 3.46678 3.45019 3.23149 3.21378 3.19776 3.18320 3.16990 3.13521 3.11882 3.10400 3.09051 3.07820 66444 37394 18767 310?8 88877 .

30、22222 52761 63811 78925 10978 55444 . 22222 2.18943 2. 18289 2.17696 2.17154 2. 16659 2.07961 2.07387 2.06816 2.06390 2.05954 12345 22222 4.32402 4.29870 4 .27540 4.25389 4.23399 4.05974 4.03820 4.01837 4.00006 3.98309 3.70661 3.68959 3.67391 3.65941 3.64596 3.43500 3.42103 3.40816 3.39624 3.38518 3

31、15772 3.14651 3.13品163.12658 3.11768 3.06691 3.05652 3.04693 3.03805 3.02980 2.77871 2. 77068 2.76326 2.75639 2.75000 2.47863 2.47266 2.46714 2.46202 2.45726 2.16203 2.15782 2.15393 2.15033 2.14697 2.05553 2.05183 2.04841 2.04523 2.04227 Uunnm且1 . 19830 4. 16722 4.13993 4.11576 4.09421 3.95265 3. 9

32、2611 3.90278 3.88210 3.86365 3.62180 3.60072 3.58215 3.56568 3.55097 3.36531 3.34793 3.33262 3.31903 3.3Co88 77131 66335 17544 08765 10000 . 33333 3.01495 3.00195 2.99049 2.98029 2.97117 2.73848 2.72839 2.71948 2.71156 2.70446 2.44818 2.44115 2.43449 2.42857 2.42326 2.14090 2.13558 2.13087 2.12667 2

33、12291 2.03693 2.03224 2.02809 2.02439 2.02108 24680 33334 4.04934 4.。14053.98556 3.96209 3.94241 a9128 18422 54003 29753 87777 . 33333 3.52025 3.49601 3.47640 3.46020 3.44660 81511 44174 11510 86432 22222 . 33333 3.03396 3.01770 3.0C451 2.99359 2. 98442 2. 95208 2.93696 2.92470 2.91455 2.90602 2.68

34、959 2.67779 2.66822 2.66028 2.65360 27820 12011 23605 10998 44333 . 22222 2. 11500 2.10872 2. 10361 2.09936 2.09578 2.01410 2.0C856 2.口04042.00030 1.99714 50505 45566 3.92568 3.89876 3.87804 3.86160 3.84824 3.71887 3.69565 3.67777 3.66358 3.65204 3.43501 3.41634 3.40194 3.39049 3.38118 3.21079 3. 19

35、526 3. 18327 3. 17374 3.16598 2. 97659 2.96395 2.95419 2.94642 2. 94009 2.89873 2.88697 2.87788 2.87065 2.86476 2.64790 2.63869 2.63157 2.62589 2.62126 2.38081 2.37387 2.36850 2.36422 2.36073 2.09273 2.08778 2.08394 2.08088 2.07839 1 . 99444 1 . 99006 1. 98667 1 98397 1.98177 70 80 90 I 00 110 3.837

36、17 3.81301 3.79706 3.77727 3.71902 3.64247 3.62157 3.60776 3. 59C 62 3.54008 3.37345 3.35657 3.34540 3.33152 3.29053 3.15954 3.14545 3.13612 3.12454 3.09023 2.93484 2.92334 2.91572 2.9C625 2.87816 2.85986 2.84915 2.84205 2.83322 2.80703 2.61742 2.6CICO 2.60342 2.59647 2.51583 2.35782 2.35146 2.34724

37、 2.34199 2.32635 2.07631 2.07176 2.06874 2.。64972.05375 1.97993 1. 97591 1. 97323 1 . 96990 1. 95996 120 150 180 240 由本在对于自由度v平日下侧概率p给出I分布的分位数f（v）。例z对fv = 20和p二0.999,可户II 5时，fp(V)7f, p（川。J:与双侧概草相I茧的分IV:数为t,（川。I, ( v l二3.5518103.55181, t, (vl t,.,120lc3.551KI仍I l、对工，F二20平口0.川2,t 0.川r( 20 I I。”日（20 I

38、flilj : GB 4086. 3-83 附录A计算方法（参考件这里给出本标准两种数值表的计算方法。在本标准所)ilj数表不能满足要求时，可参考这些策法及附录B的程序进行计算，或者使用插值方法作粗略计算。A .1 t分布的定义与记号自由度为咐甘t分布的密度函数是f+ 2 p (t川）= J.f (I，川I,与下假lj概率P对应的分位数tp ( v）满足如下方程zP(lp(V);V）二P。注：t分布在自由度v时的极限分布为正态分布。A .2 分布与t分布的关系A .2 .1 分布的定义与记号参数为，b的分布的密度函数是-oo .I oc, , f（X;a,b）丁卉丁；x0l (-xJ 1, o

39、言乱P 2c cdui (l-d)2-duJ,. 式中：俨二l户，c= gb d= _J_ ga 13“ 一一一GB 4086.3-83 B .1 附录计算程序( i；号iI) B 说明这w给址：J+jf木标准实际计悍的四个fGO TO 80 Cl IY0096 70 CONTINUE Bfl.(009! BETXOOi8 C,BETX0105 BEXOID BEJX0107 BETXOI08 BETXOI日PB二TX0110BFTXOlll 8ETXOl12 日ETXO 115 8fTX011句BtTXOI,) BEXQ1 :o BEIXOll, 己干rxo1 s 日仁川O！飞QBETJ,

40、c ,O 6fiX0121 11r,1x01；、lllTXOi，人BFT页。l川+ + + + + + cc C白LLNCR!O(l.00-P.EPS.U.IER) 白1.000 (2.000/(9.口DO*f 18=1.000 (2.0日（9.000tf2)C = BB - (1.0DO -Bl末UtUD = OSQRTCA*A*(l.000-8 CCl .ODO All X = ( IA*B + U末日）；术380 CONTINLE x = f2/(f2 + fl日向BSOOENS IF ROOT .LE. O.OCO) R DENS/ODENS If CROOl G丁.0.000) R

41、R/CDENS 口SQRTCROOll)X = X R GB 4086. 3-83 HN=MN+l IF MN .GT. 10) G口TO100 IF CD向BSCRl.GT. EPSl GO TO 90 100 CONTINUE RETURN END BETX0125 BETX0126 BE1X0127 日FTX0128BETX0129 日ETXOllO C TFOCOOI C= TFOOOCOZ C !FOOi OC3SUBROUTINE TFDP IF CT .GT. O.ODOl P = 1.0DD - P 20 CONTINUE RETURN END TFOOC036 lfOOOOl

42、l Tf 000038 Tf 000039 TF000040 TF000041 TF000042 Tf 000043 TF000044 lf000045 TF000046 Tf000047 TFOCCQi,8 : I 12 GB 4086.3-83 C TXOOOOO I C= = = = TXO C OC 02 C TXOLDC03 SUBROUTINE TXQ(P,N.EPS.T,JERl TXOCCCO句INTEGER N.IER TXOC；旧OSDOUBLE PRECISION P.EPS.T TXOCCCG6 C TXOllOC07 C * PURPOSE * TX000008 C

43、PERCENTAGE POINT OF T DISTRIBUTION TX000009 C TXOOOOIO C * ARGUMENTS * TX000011 C ON ENTRY lX000012 C N DEGREES OF FREEDOM TXOCC013 C P LOWER PROB向日ll!TYTXOCC014 C EPS REQUIRED PRECISION lXOOC015 C ON RETURN TXOCCC 16 C T PERCENTAGE POINT TXOCCC17 C IER ERROR P内RAMETERxoc018 C IER.NE.O INDICATES P .

44、LE.O OR P .GE.1 IX00009 C TX000020 C * REQUIRED ROUTINES * TXOOOOZI C NORFO DISTRIBUTION FUNCTION OF NORMAL DISTRIBUTION TX000022 C NORXD PERCENTAGE POINT OF NORMAL DISTRIBUTION TX000023 C BETAFD DISTRIBUTION FUNCTION OF BETA OISTRIBUIION TX000024 C BET内XOPERCENT白GEPOINT OF BET内DISTRIBUTIONTX000025

45、C TXOJC026 c 事本ALGORITHM* TX000027 C FOR P=0.5. TX000028 C T(P,Nl = Q. 1X000029 C FOR P .NE .0 .5. TXOOOOlO C TCP.NJ= CSQRTCNIXP1.N/2,1/2l-NJ. TXOCC031 C WHERE TX000032 C C = 1, Pl= 2(1-P). FOR P.GT.0.5. TXOCC033 C C = 1. Pl = Z*P FOR P.LT.0.5. TX000034 C X IS白PERCENTAGEPOINT OF BETA DISTRIBUTION. T

46、X000035 C lX000036 C一一一一- 一一一一一一一- - 一一一一一一岛TXQC037C TXOC:031 c c c 。OUBLEPRECISION FN.PP TXOC0039 IER = 0 IF P GT.。.000.AND. P .LT. 1.000) GO TO 10 !ER = 129 T = 1.0D90S!GN(1.0日（，p0.5日（）GO TO 30 10 CONTINUE IF (p .NE. 0.5日0)GO 10 20 T = 0.000 GO TO 30 20 CONTINUE FN = N pp = 2.000本PIF P .GT. 0.500)

47、 PP = 2.000 PP CALL BETAXO(PP.N.1.EPS.T.IERJ T = DSQRT(1.000-TlFN/Tl IF P .LT .0.500) T = -T 30 CONTINUE RETURN ENO TXOCCC40 TXOO.CI TXC臼0042TXD00043 TX000044 1X000045 l X000046 TX000041 TXCCC D乌ETXOOOOl9 TXO丁C050 TXOCC01 TXODC:J52 1X000053 TX000054 TX000055 TXOOG05己TX00005 i TXOOOOS久以0CJC59TX000060 fX000061 GB 4086.3-83 也tfJ 苦￥J /J 丰出口U伴儿丢4KT rL丁咔JJ7！ Hiin 归田术人4Af4Jr1口zj委委术术使技ott毅准准公际标陆明用用L川川一L叫川尘uhJI 法法日力为vm汁计人统统的rL叫妃1儿k注明山阳川仁说悄悄叩准加仁mu怀仁怦附丰i非本