Some standard content:
National Standard of the People's Republic of China
Numerical tables of statistical distributions
Normal distribution
Tables for statistical distributionsNormal distribution
UDC 311.13(083.5)
GB 4086.1--83
This standard includes three numerical tables of normal distribution commonly used in statistics. Their names, table distances and precisions are as follows:Normal distribution density function table
Normal distribution function table
Normal distribution quantile table
u=0 (0.01)4.99
u=0 (0.01)4.99
p=0.5(0.001)0.999
6 decimal places
6 decimal places
6 decimal places
The normal distribution referred to in this standard is the standard normal distribution. The quantiles in the table correspond to the lower probability. Although 6 decimal places are given in the table, the number of decimal places to be used in use depends on the actual problem. If the requirements cannot be met in the application, refer to the processing method in the appendix. Issued by the National Bureau of Standards in 1983-1221
Implementation from 1984 to 1001
Normal distribution density function table
133383
381388
352069
194186
110921
1398922
390242
310060
287369
191860
0147639
0,000191
.000015
398862
285034
189543
125665
107406||tt ||0+063157
000271
000015
GB 4086.1—83
398763
346668
282694
258881
234714
143505
123763
089333
026426||tt| |002165
.000079||tt| |000014
398623
344818
232297
162555
121878
103961
.009347
.000076
8:000005
This table gives the value of (u) in the normal distribution density function for u. Example: For u=3.08, (u)=0.003475. 0.05
398444
342944
120009
.059595
.031740
to change
203571
118157
084776||tt ||.000070
.000005
397966
393219
318737
178104
1001364
000681
397668
270864||tt ||198863
1145 05 | | tt | | 068144 | 02
151853||tt| |884930
.977250
995339
996533
997445
999032
999767
999892
999928
999987
999991
.999998
000000
791030
886861
986447
989556
998193
999065
999896
999980
999987|| tt||.999999
5 87064
793892
922196
996736
997599
999933
9Q9971
999988
999992
999997
999 998
1590954||t t||629300
966375
8:990099
999381
999566
999792
999858
999936
999982
999988|| tt||594835
7703 50
925066
959070
994457
Q:996928
999155
1999938
999983
.999989
8:999998
This table gives the value of u in the normal distribution. Example: For u-1.33, Φ(u)=0.908241.91
598706
911492
939429
950529
967843
994614
.995975
99702 0
.999596
.999720
.999807
7453 73 | | tt | 961
999999
.644309
8:991166
751 748 | | tt | | 899727 | 997365
998074
999758
0.3999986
Normal distribution quantile table
100434
279319
1305481
358459
385320
524401
674490
706303
738847
9 94458
136431
.405072
475791
.644854
750686
\2du-p
027576
230118
255936
281926
334503||tt| |0 361133
0498687
527279
556308
585815
677640
742144
.919183||tt| |040732
131131
231864
762410
055174
156042
258527
.530161
712751
745450
135896
GB 4086.1--83
082813
158580
339809
562170||tt ||926859
.29883
1359463
1-425544
674665
035100
110516
.263714| |tt||535940
565108
365808
589268
2:144411
512144
本装对了下拉可以p分止态态成的分位数up。例：可以p0.95，up=1.644854。p1.5时，up-
。例：
与双拉性总分位数的u
0. 510073
755415
11439531
170090
1.281552。
Q:428895
0512930
.541737||tt ||725737
938476
.378659
1446632
706043
825007
197286
092879||tt| |271508
404289
530068
995393
对 -α= 0.05, u1 -4 2 = uu.375 - 1.959964例：
Q: 57691
765456
.870550
461056
538199
625763
.727934
852180
.097915
199336
250760
.276714
329206
355787
.382622
.409735||tt ||:493018
0:579873
.703089
735558
768820
838055
874217
911561| |tt||990356
.07583
170002
.398377
.546433
635234
739198
866296
GB4086.1—83
附能A
calculation method
（参考件）
这是电影本标准毕业手机表的设计。 A.1 definition与记号
本所指的止态性分是standard正态性性，其densityfunction是b（u）
推态推发是
Φ(u)(u)(
写下拉发动p可以分位数up 使用最新最好动画：1
A.2 设计方法
(u)du。
du=p，
(up)-=0。||tt ||A.2.1 正态性电视发的电视的电视
真接按发动电视。
A，2.2 正态性流设备的电视的电视
用连分式遥近：| |tt||当03时有
当u3时有
r1-G（u)，当u≥0,
G(uj),
当uo。
式的正解的正解内容分分式的长数。A.2.3正态成分分位数的数字的
GB4086.1—83
使用A ... tt||上式的公司的这些通过4.9×10-4。A.3分位数的选代设计
5.7262204
y+11.640595),
电影，可以一个分位数的分位数的分位数的公式所所以可以可以可以可以分位数所可以可以分分数。 As the initial value.根法设计安全的分位数。 The process is as follows：
我们，把分位数所使用的字作记的F(r=0,
r=ro +。| |tt||在上海对F（α)作二阦台劳列分0=F(α) =F(αa+△)
F(co) + F(xo)A+ F\(o)-
解之得
或等了地有
-F(xo)±V(F(x0))?-2F(ro)F\(ao)F\( co)
2F(ro)
F(xo)FV(F(2o))?-2F(xo)F(ro) Accordingly |F(αo)
此外，根号的正老号正视应电影△|了小。亦即当F（α）>0时，式中国家的根号取正（或分母根号取根号)；当F（α)<0时，4式中国全的根号take根号（或分母根号take正）. 1 英语正视通过。97
B.1 设计
GB 4086.1--83
附能B
电影电视
（参考件）|| tt|| Here are the two FORTRAN language programs used for the actual calculation of this standard. Calculating method 见附若A，
However, the standard standard is 10~10 programs. ||DOUBLE PRECISION U,P
** PURPOSE **
DISTRIBUTION FUNCTION OF NORMAL DISTRIBUTION** ARGUMENTS **
ON ENTRY
NORMAL DEVIATE
ON RETURN
LOWER PROBABILITY
** REQUIRED ROUTINES **
** ALGORITHM **
FOR NEGATIVE U
P(U) = PP(ABS(U)),
FOR NON-NEGATIVE U
P(U) = 1 - PP(U),
FOR U.GT.3
PP(U) = EXP(-U**2/2)/SQRT(2*PAI)*(1/U.+.1/U,+.2/U.+.+.k/U.+..+.).
NORF0001
NORF0002
NORF0003
NORF0004
NORFO005
NORF0006
NORF0007
NORF0008
NGRF0009
NORFO010
NORF0011
NORFO012
NORF0013
NORF0014
NORF0015
NORF0016
NORF0017
NORF0018
NORF0019
NORF0020
NORF0021
NORF0022
NDRF0023
NORF0024
(1) NORFO025
FOR U.GE.0 AND U.LE.3
PP(U)= 0.5 - EXP(-U**2/2)/SQRT(2*PAI)*(U/1.-.U**2/3.+。2*U**2/5..3*U**2/7.+.*.).
WHERE.+. AND.-. DENOTE CONTINUED FRACTIONINTEGER K
DOUBLE PRECISION Y.Y2,Z.FJ,S,BDATA K/28/S/~1.0D0/，B/3.000/Y = BABS(U)
Y2 = Y*Y
Z DEXP(-0.5D0*Y2)*0.39894228040143267800P = 0.0DO
IF(Y.LE.B)GO TO 20
NORF0026
NORF0027
(2) NORF0028
NORF0029
NORF0030
NORFO031
NORF0032
NORF0033
NORFO034
NORF0035
NORF0036
NORF0037
NORF0038
NORFC039
NORFO040
NORF0041
NORF0042
GB4086.1-83
FORMULA (1) IS EMPLOYEO FOR LARGE UDO 10 I=1.K
P = FJ/(Y + P)
FJ = FJ - 1.0D0
CONTINUE
P = Z/(Y
GO TO 40
20 CONTINUE
FORMULA (2) IS EMPLOYEO FOR SMALL U00 30 1 = 1.K
P = FJ*Y2/(2.0DO*FJ + 1.0D0 + S*P)s=s
FJ FJ －
CONTINUE
Z*Y/(1.000- P)
P = 0.500 -
40 CONTINUE
IF(U.GT. 0.0DO) P = 1.ODO~P
RETURN
NDRF0043
NORFO044
NORF0045
NORF0046
NORF0047
NORF0048
NORF0049
NORF0050wwW.bzxz.Net
NORF0051
NORF0052
NORF0053
NORF0054
NORF0055
NORF0056
NDRI0057
NURF0058
NORF0059
NURFC060
NORF0061
NORF0062
NORI0063
NORF0064
NORF0065
NURF0066
GB 4086.1-83
SUBROUTINE NORXO(P,EPS.U,IER)INTEGER IER
DOUBLE PRECISION P,EPS,U
** PURPOSE **
PERCENTAGE POINT OF NORMAL DISTRIBUTION** ARGUMENTS **
ONENTRY
ON RETURN
LOWER PROBABILITY
REQUIRED PRECISION
PERCENTAGE POINT
ERROR PARAMETER
IER.NE.O INDICATES P.LE.O OR P.GE.1** REQUIRED ROUTINES **
DISTRIBUTION FUNCTION OF NORMAL DISTRIBUTION** ALGORITHM **
FOR P=O.5,
FOR P,NE.O.S, HITOTUMATU-S ITERATION METHOD IS USEO.INITIAL VALUE IS CALCULATED BY YAMAUTI-S FORMULA,U(P) = C*SQRT(Y*(2.0611786-5.7262204/(Y+11.640595))),WHERE
Y = -ln(P*(1-p)*4),
FOR P.GT.0.5,
C = 1,
C =-1,
FOR P.Lt.0.5.
INTEGER MN
DOUBLE PRECISION R.PP.ROOT.Y,DENS,DDENSIER 0
IF
NORF0001
NORF0002
NORF0003
NORF0004
NORFO005
NORF0006
NORF0007
NORF0008
NGRF0009
NORFO010
NORF0011
NORFO012
NORF0013
NORF0014
NORF0015
NORF0016
NORF0017
NORF0018
NORF0019
NORF0020
NORF0021
NORF0022
NDRF0023
NORF0024
(1) NORFO025
FOR U.GE.0 AND U.LE.3
PP(U)= 0.5 - EXP(-U**2/2)/SQRT(2*PAI)*(U/1.-.U**2/3.+。2*U**2/5..3*U**2/7.+.*.).
WHERE.+. AND.-. DENOTE CONTINUED FRACTIONINTEGER K
DOUBLE PRECISION Y.Y2,Z.FJ,S,BDATA K/28/S/~1.0D0/，B/3.000/Y = BABS(U)
Y2 = Y*Y
Z DEXP(-0.5D0*Y2)*0.39894228040143267800P = 0.0DO
IF(Y.LE.B)GO TO 20
NORF0026
NORF0027
(2) NORF0028
NORF0029
NORF0030
NORFO031
NORF0032
NORF0033
NORFO034
NORF0035
NORF0036
NORF0037
NORF0038
NORFC039
NORFO040
NORF0041
NORF0042
GB4086.1-83
FORMULA (1) IS EMPLOYEO FOR LARGE UDO 10 I=1.K
P = FJ/(Y + P)
FJ = FJ - 1.0D0
CONTINUE
P = Z/(Y
GO TO 40
20 CONTINUE
FORMULA (2) IS EMPLOYEO FOR SMALL U00 30 1 = 1.K
P = FJ*Y2/(2.0DO*FJ + 1.0D0 + S*P)s=s
FJ FJ －
CONTINUE
Z*Y/(1.000- P)
P = 0.500 -
40 CONTINUE
IF(U.GT. 0.0DO) P = 1.ODO~P
RETURN
NDRF0043
NORFO044
NORF0045
NORF0046
NORF0047
NORF0048
NORF0049
NORF0050
NORF0051
NORF0052
NORF0053
NORF0054
NORF0055
NORF0056
NDRI0057
NURF0058
NORF0059
NURFC060
NORF0061
NORF0062
NORI0063
NORF0064
NORF0065
NURF0066
GB 4086.1-83
SUBROUTINE NORXO(P,EPS.U,IER)INTEGER IER
DOUBLE PRECISION P,EPS,U
** PURPOSE **
PERCENTAGE POINT OF NORMAL DISTRIBUTION** ARGUMENTS **
ONENTRY
ON RETURN
LOWER PROBABILITY
REQUIRED PRECISION
PERCENTAGE POINT
ERROR PARAMETER
IER.NE.O INDICATES P.LE.O OR P.GE.1** REQUIRED ROUTINES **
DISTRIBUTION FUNCTION OF NORMAL DISTRIBUTION** ALGORITHM **
FOR P=O.5,
FOR P,NE.O.S, HITOTUMATU-S ITERATION METHOD IS USEO.INITIAL VALUE IS CALCULATED BY YAMAUTI-S FORMULA,U(P) = C*SQRT(Y*(2.0611786-5.7262204/(Y+11.640595))),WHERE
Y = -ln(P*(1-p)*4),
FOR P.GT.0.5,
C = 1,
C =-1,
FOR P.Lt.0.5.
INTEGER MN
DOUBLE PRECISION R.PP.ROOT.Y,DENS,DDENSIER 0
IF
NORF0001
NORF0002
NORF0003
NORF0004
NORFO005
NORF0006
NORF0007
NORF0008
NGRF0009
NORFO010
NORF0011
NORFO012
NORF0013
NORF0014
NORF0015
NORF0016
NORF0017
NORF0018
NORF0019
NORF0020
NORF0021
NORF0022
NDRF0023
NORF0024
(1) NORFO025
FOR U.GE.0 AND U.LE.3
PP(U)= 0.5 - EXP(-U**2/2)/SQRT(2*PAI)*(U/1.-.U**2/3.+。2*U**2/5..3*U**2/7.+.*.).
WHERE.+. AND.-. DENOTE CONTINUED FRACTIONINTEGER K
DOUBLE PRECISION Y.Y2,Z.FJ,S,BDATA K/28/S/~1.0D0/，B/3.000/Y = BABS(U)
Y2 = Y*Y
Z DEXP(-0.5D0*Y2)*0.39894228040143267800P = 0.0DO
IF(Y.LE.B)GO TO 20
NORF0026
NORF0027
(2) NORF0028
NORF0029
NORF0030
NORFO031
NORF0032
NORF0033
NORFO034
NORF0035
NORF0036
NORF0037
NORF0038
NORFC039
NORFO040
NORF0041
NORF0042
GB4086.1-83
FORMULA (1) IS EMPLOYEO FOR LARGE UDO 10 I=1.K
P = FJ/(Y + P)
FJ = FJ - 1.0D0
CONTINUE
P = Z/(Y
GO TO 40
20 CONTINUE
FORMULA (2) IS EMPLOYEO FOR SMALL U00 30 1 = 1.K
P = FJ*Y2/(2.0DO*FJ + 1.0D0 + S*P)s=s
FJ FJ －
CONTINUE
Z*Y/(1.000- P)
P = 0.500 -
40 CONTINUE
IF(U.GT. 0.0DO) P = 1.ODO~P
RETURN
NDRF0043
NORFO044
NORF0045
NORF0046
NORF0047
NORF0048
NORF0049
NORF0050
NORF0051
NORF0052
NORF0053
NORF0054
NORF0055
NORF0056
NDRI0057
NURF0058
NORF0059
NURFC060
NORF0061
NORF0062
NORI0063
NORF0064
NORF0065
NURF0066
GB 4086.1-83
SUBROUTINE NORXO(P,EPS.U,IER)INTEGER IER
DOUBLE PRECISION P,EPS,U
** PURPOSE **
PERCENTAGE POINT OF NORMAL DISTRIBUTION** ARGUMENTS **
ONENTRY
ON RETURN
LOWER PROBABILITY
REQUIRED PRECISION
PERCENTAGE POINT
ERROR PARAMETER
IER.NE.O INDICATES P.LE.O OR P.GE.1** REQUIRED ROUTINES **
DISTRIBUTION FUNCTION OF NORMAL DISTRIBUTION** ALGORITHM **
FOR P=O.5,
FOR P,NE.O.S, HITOTUMATU-S ITERATION METHOD IS USEO.INITIAL VALUE IS CALCULATED BY YAMAUTI-S FORMULA,U(P) = C*SQRT(Y*(2.0611786-5.7262204/(Y+11.640595))),WHERE
Y = -ln(P*(1-p)*4),
FOR P.GT.0.5,
C = 1,
C =-1,
FOR P.Lt.0.5.
INTEGER MN
DOUBLE PRECISION R.PP.ROOT.Y,DENS,DDENSIER 0
IFB)GO TO 20
NORF0026
NORF0027
(2) NORF0028
NORF0029
NORF0030
NORFO031
NORF0032
NORF0033
NORFO034
NORF0035
NORF0036
NORF0037
NORF0038
NORFC039
NORFO040
NORF0041
NORF0042
GB4086.1-83
FORMULA (1) IS EMPLOYEO FOR LARGE UDO 10 I=1.K
P = FJ/(Y + P)
FJ = FJ - 1.0D0
CONTINUE
P = Z/(Y
GO TO 40
20 CONTINUE
FORMULA (2) IS EMPLOYEO FOR SMALL U00 30 1 = 1.K
P = FJ*Y2/(2.0DO*FJ + 1.0D0 + S*P)s=s
FJ FJ －
CONTINUE
Z*Y/(1.000- P)
P = 0.500 -
40 CONTINUE
IF(U.GT. 0.0DO) P = 1.ODO~P
RETURN
NDRF0043
NORFO044
NORF0045
NORF0046
NORF0047
NORF0048
NORF0049
NORF0050
NORF0051
NORF0052
NORF0053
NORF0054
NORF0055
NORF0056
NDRI0057
NURF0058
NORF0059
NURFC060
NORF0061
NORF0062
NORI0063
NORF0064
NORF0065
NURF0066
GB 4086.1-83
SUBROUTINE NORXO(P,EPS.U,IER)INTEGER IER
DOUBLE PRECISION P,EPS,U
** PURPOSE **
PERCENTAGE POINT OF NORMAL DISTRIBUTION** ARGUMENTS **
ONENTRY
ON RETURN
LOWER PROBABILITY
REQUIRED PRECISION
PERCENTAGE POINT
ERROR PARAMETER
IER.NE.O INDICATES P.LE.O OR P.GE.1** REQUIRED ROUTINES **
DISTRIBUTION FUNCTION OF NORMAL DISTRIBUTION** ALGORITHM **
FOR P=O.5,
FOR P,NE.O.S, HITOTUMATU-S ITERATION METHOD IS USEO.INITIAL VALUE IS CALCULATED BY YAMAUTI-S FORMULA,U(P) = C*SQRT(Y*(2.0611786-5.7262204/(Y+11.640595))),WHERE
Y = -ln(P*(1-p)*4),
FOR P.GT.0.5,
C = 1,
C =-1,
FOR P.Lt.0.5.
INTEGER MN
DOUBLE PRECISION R.PP.ROOT.Y,DENS,DDENSIER 0
IFB)GO TO 20
NORF0026
NORF0027
(2) NORF0028
NORF0029
NORF0030
NORFO031
NORF0032
NORF0033
NORFO034
NORF0035
NORF0036
NORF0037
NORF0038
NORFC039
NORFO040
NORF0041
NORF0042
GB4086.1-83
FORMULA (1) IS EMPLOYEO FOR LARGE UDO 10 I=1.K
P = FJ/(Y + P)
FJ = FJ - 1.0D0
CONTINUE
P = Z/(Y
GO TO 40
20 CONTINUE
FORMULA (2) IS EMPLOYEO FOR SMALL U00 30 1 = 1.K
P = FJ*Y2/(2.0DO*FJ + 1.0D0 + S*P)s=s
FJ FJ －
CONTINUE
Z*Y/(1.000- P)
P = 0.500 -
40 CONTINUE
IF(U.GT. 0.0DO) P = 1.ODO~P
RETURN
NDRF0043
NORFO044
NORF0045
NORF0046
NORF0047
NORF0048
NORF0049
NORF0050
NORF0051
NORF0052
NORF0053
NORF0054
NORF0055
NORF0056
NDRI0057
NURF0058
NORF0059
NURFC060
NORF0061
NORF0062
NORI0063
NORF0064
NORF0065
NURF0066
GB 4086.1-83
SUBROUTINE NORXO(P,EPS.U,IER)INTEGER IER
DOUBLE PRECISION P,EPS,U
** PURPOSE **
PERCENTAGE POINT OF NORMAL DISTRIBUTION** ARGUMENTS **
ONENTRY
ON RETURN
LOWER PROBABILITY
REQUIRED PRECISION
PERCENTAGE POINT
ERROR PARAMETER
IER.NE.O INDICATES P.LE.O OR P.GE.1** REQUIRED ROUTINES **
DISTRIBUTION FUNCTION OF NORMAL DISTRIBUTION** ALGORITHM **
FOR P=O.5,
FOR P,NE.O.S, HITOTUMATU-S ITERATION METHOD IS USEO.INITIAL VALUE IS CALCULATED BY YAMAUTI-S FORMULA,U(P) = C*SQRT(Y*(2.0611786-5.7262204/(Y+11.640595))),WHERE
Y = -ln(P*(1-p)*4),
FOR P.GT.0.5,
C = 1,
C =-1,
FOR P.Lt.0.5.
INTEGER MN
DOUBLE PRECISION R.PP.ROOT.Y,DENS,DDENSIER 0
IFINITIAL VALUE IS CALCULATED BY YAMAUTI-S FORMULA,U(P) = C*SQRT(Y*(2.0611786-5.7262204/(Y+11.640595))),WHERE
Y = -ln(P*(1-p)*4),
FOR P.GT.0.5,
C = 1,
C =-1,
FOR P.Lt.0.5.
INTEGER MN
DOUBLE PRECISION R.PP.ROOT.Y,DENS,DDENSIER 0
IFINITIAL VALUE IS CALCULATED BY YAMAUTI-S FORMULA,U(P) = C*SQRT(Y*(2.0611786-5.7262204/(Y+11.640595))),WHERE
Y = -ln(P*(1-p)*4),
FOR P.GT.0.5,
C = 1,
C =-1,
FOR P.Lt.0.5.
INTEGER MN
DOUBLE PRECISION R.PP.ROOT.Y,DENS,DDENSIER 0
IF
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