In [55]:
from scipy import stats as st
import numpy as np
alp=[0.1,0.05,0.02,0.01,0.005]
colname=["%.1f%%"%(a*100) for a in alp]

t (Student) rozdělení

kvantily pro $t(n)$

In [54]:
import pandas as pd
ns=range(3,51)
df=pd.DataFrame(np.array([st.t(n).isf(alp) for n in ns]),columns=colname)
df.rename(index=dict(enumerate(ns)))
Out[54]:
10.0% 5.0% 2.0% 1.0% 0.5%
3 1.637744 2.353363 3.481909 4.540703 5.840909
4 1.533206 2.131847 2.998528 3.746947 4.604095
5 1.475884 2.015048 2.756509 3.364930 4.032143
6 1.439756 1.943180 2.612242 3.142668 3.707428
7 1.414924 1.894579 2.516752 2.997952 3.499483
8 1.396815 1.859548 2.448985 2.896459 3.355387
9 1.383029 1.833113 2.398441 2.821438 3.249836
10 1.372184 1.812461 2.359315 2.763769 3.169273
11 1.363430 1.795885 2.328140 2.718079 3.105807
12 1.356217 1.782288 2.302722 2.680998 3.054540
13 1.350171 1.770933 2.281604 2.650309 3.012276
14 1.345030 1.761310 2.263781 2.624494 2.976843
15 1.340606 1.753050 2.248540 2.602480 2.946713
16 1.336757 1.745884 2.235358 2.583487 2.920782
17 1.333379 1.739607 2.223845 2.566934 2.898231
18 1.330391 1.734064 2.213703 2.552380 2.878440
19 1.327728 1.729133 2.204701 2.539483 2.860935
20 1.325341 1.724718 2.196658 2.527977 2.845340
21 1.323188 1.720743 2.189427 2.517648 2.831360
22 1.321237 1.717144 2.182893 2.508325 2.818756
23 1.319460 1.713872 2.176958 2.499867 2.807336
24 1.317836 1.710882 2.171545 2.492159 2.796940
25 1.316345 1.708141 2.166587 2.485107 2.787436
26 1.314972 1.705618 2.162029 2.478630 2.778715
27 1.313703 1.703288 2.157825 2.472660 2.770683
28 1.312527 1.701131 2.153935 2.467140 2.763262
29 1.311434 1.699127 2.150325 2.462021 2.756386
30 1.310415 1.697261 2.146966 2.457262 2.749996
31 1.309464 1.695519 2.143833 2.452824 2.744042
32 1.308573 1.693889 2.140904 2.448678 2.738481
33 1.307737 1.692360 2.138159 2.444794 2.733277
34 1.306952 1.690924 2.135581 2.441150 2.728394
35 1.306212 1.689572 2.133157 2.437723 2.723806
36 1.305514 1.688298 2.130871 2.434494 2.719485
37 1.304854 1.687094 2.128714 2.431447 2.715409
38 1.304230 1.685954 2.126674 2.428568 2.711558
39 1.303639 1.684875 2.124742 2.425841 2.707913
40 1.303077 1.683851 2.122910 2.423257 2.704459
41 1.302543 1.682878 2.121170 2.420803 2.701181
42 1.302035 1.681952 2.119515 2.418470 2.698066
43 1.301552 1.681071 2.117940 2.416250 2.695102
44 1.301090 1.680230 2.116438 2.414134 2.692278
45 1.300649 1.679427 2.115005 2.412116 2.689585
46 1.300228 1.678660 2.113636 2.410188 2.687013
47 1.299825 1.677927 2.112327 2.408345 2.684556
48 1.299439 1.677224 2.111073 2.406581 2.682204
49 1.299069 1.676551 2.109873 2.404892 2.679952
50 1.298714 1.675905 2.108721 2.403272 2.677793

F (Fisher-Snedecor) rozdělení

kvantily pro $F(n,n)$ (stejně velké vzorky)

In [58]:
import pandas as pd
df=pd.DataFrame(np.array([st.f(n,n).isf(alp) for n in ns[2:]]),columns=colname)
df.rename(index=dict(enumerate(ns[2:])))
Out[58]:
10.0% 5.0% 2.0% 1.0% 0.5%
5 3.452982 5.050329 7.952932 10.967021 14.939605
6 3.054551 4.283866 6.392778 8.466125 11.073039
7 2.784930 3.787044 5.435476 6.992833 8.885389
8 2.589349 3.438101 4.789995 6.028870 7.495906
9 2.440340 3.178893 4.325487 5.351129 6.541090
10 2.322604 2.978237 3.974972 4.849147 5.846678
11 2.226930 2.817930 3.700781 4.462436 5.319667
12 2.147437 2.686637 3.480166 4.155258 4.906249
13 2.080185 2.576927 3.298599 3.905204 4.573279
14 2.022434 2.483726 3.146376 3.697541 4.299287
15 1.972216 2.403447 3.016768 3.522194 4.069785
16 1.928079 2.333484 2.904969 3.372046 3.874654
17 1.888929 2.271893 2.807449 3.241930 3.706622
18 1.853923 2.217197 2.721560 3.128006 3.560332
19 1.822403 2.168252 2.645274 3.027358 3.431750
20 1.793843 2.124155 2.577015 2.937735 3.317786
21 1.767823 2.084189 2.515535 2.857371 3.216028
22 1.743999 2.047770 2.459836 2.784859 3.124572
23 1.722088 2.014425 2.409108 2.719068 3.041889
24 1.701854 1.983760 2.362688 2.659072 2.966742
25 1.683101 1.955447 2.320026 2.604113 2.898116
26 1.665661 1.929213 2.280665 2.553560 2.835173
27 1.649393 1.904823 2.244219 2.506883 2.777213
28 1.634174 1.882079 2.210362 2.463636 2.723648
29 1.619900 1.860811 2.178814 2.423439 2.673979
30 1.606479 1.840872 2.149335 2.385967 2.627781
31 1.593832 1.822132 2.121719 2.350941 2.584689
32 1.581890 1.804482 2.095786 2.318118 2.544388
33 1.570591 1.787822 2.071378 2.287288 2.506606
34 1.559881 1.772066 2.048358 2.258266 2.471103
35 1.549712 1.757140 2.026605 2.230890 2.437672
36 1.540040 1.742973 2.006011 2.205018 2.406127
37 1.530829 1.729507 1.986481 2.180523 2.376308
38 1.522042 1.716687 1.967930 2.157292 2.348070
39 1.513650 1.704465 1.950282 2.135225 2.321286
40 1.505625 1.692797 1.933470 2.114232 2.295839
41 1.497941 1.681644 1.917431 2.094234 2.271629
42 1.490575 1.670971 1.902110 2.075156 2.248563
43 1.483506 1.660744 1.887458 2.056934 2.226558
44 1.476716 1.650935 1.873430 2.039508 2.205538
45 1.470187 1.641516 1.859982 2.022824 2.185436
46 1.463902 1.632464 1.847079 2.006834 2.166190
47 1.457849 1.623755 1.834686 1.991492 2.147743
48 1.452012 1.615370 1.822770 1.976757 2.130044
49 1.446381 1.607289 1.811305 1.962593 2.113047
50 1.440942 1.599495 1.800262 1.948964 2.096708

kvantily pro $F(n,n+1)$ (přidání parametru)

In [57]:
df=pd.DataFrame(np.array([st.f(n,n+1).isf(alp) for n in ns[2:]]),columns=colname)
df.rename(index=dict(enumerate(ns[2:])))
Out[57]:
10.0% 5.0% 2.0% 1.0% 0.5%
5 3.107512 4.387374 6.584743 8.745895 11.463696
6 2.827392 3.865969 5.575612 7.191405 9.155336
7 2.624135 3.500464 4.897197 6.177624 7.694143
8 2.469406 3.229583 4.410456 5.467123 6.693300
9 2.347306 3.020383 4.044201 4.942421 5.967570
10 2.248230 2.853625 3.758439 4.539282 5.418259
11 2.166031 2.717331 3.529052 4.219820 4.988377
12 2.096588 2.603661 3.340664 3.960326 4.642890
13 2.037038 2.507263 3.183024 3.745241 4.359146
14 1.985321 2.424364 3.049036 3.563943 4.121889
15 1.939921 2.352223 2.933640 3.408947 3.920483
16 1.899696 2.288800 2.833127 3.274823 3.747297
17 1.863766 2.232546 2.744717 3.157545 3.596716
18 1.831444 2.182263 2.666287 3.054058 3.464522
19 1.802185 2.137009 2.596187 2.962011 3.347485
20 1.775551 2.096033 2.533112 2.879556 3.243091
21 1.751183 2.058728 2.476023 2.805229 3.149352
22 1.728788 2.024600 2.424073 2.737849 3.064681
23 1.708123 1.993239 2.376574 2.676456 2.987789
24 1.688981 1.964306 2.332955 2.620260 2.917623
25 1.671191 1.937514 2.292738 2.568605 2.853313
26 1.654606 1.912622 2.255525 2.520943 2.794133
27 1.639099 1.889424 2.220977 2.476810 2.739475
28 1.624562 1.867744 2.188803 2.435815 2.688822
29 1.610901 1.847428 2.158757 2.397620 2.641735
30 1.598034 1.828345 2.130624 2.361937 2.597836
31 1.585889 1.810379 2.104219 2.328515 2.556802
32 1.574402 1.793429 2.079378 2.297136 2.518349
33 1.563519 1.777407 2.055960 2.267611 2.482233
34 1.553189 1.762233 2.033840 2.239773 2.448238
35 1.543369 1.747838 2.012908 2.213474 2.416174
36 1.534018 1.734160 1.993064 2.188585 2.385876
37 1.525102 1.721142 1.974222 2.164988 2.357196
38 1.516589 1.708736 1.956304 2.142582 2.330000
39 1.508450 1.696896 1.939239 2.121274 2.304172
40 1.500659 1.685582 1.922965 2.100981 2.279606
41 1.493193 1.674758 1.907424 2.081629 2.256208
42 1.486031 1.664389 1.892566 2.063150 2.233893
43 1.479152 1.654447 1.878344 2.045483 2.212583
44 1.472539 1.644904 1.864714 2.028573 2.192209
45 1.466176 1.635733 1.851640 2.012370 2.172708
46 1.460048 1.626913 1.839086 1.996828 2.154021
47 1.454141 1.618423 1.827018 1.981905 2.136097
48 1.448442 1.610242 1.815409 1.967563 2.118886
49 1.442940 1.602354 1.804230 1.953766 2.102346
50 1.437624 1.594741 1.793457 1.940483 2.086435
In [35]:
np.sqrt(15*14*3**2+5*4*5**2)
Out[35]:
48.887626246321268
In [36]:
np.sqrt(15*6)
Out[36]:
9.4868329805051381
In [37]:
np.sqrt(15*6*19/21.)
Out[37]:
9.0237781127735754
In [41]:
st.norm().isf(0.025)
Out[41]:
1.9599639845400545
In [43]:
5/np.sqrt(9+25)
Out[43]:
0.8574929257125441