Demo of noncentral distributions.
| ... from pacal import *
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Using compiled interpolation routine Compiled sparse grid routine not available
| ... from pylab import figure, legend, title, xlim, ylim
colors = "kbgrcmy"
def plot_nonc(d, titl = "", lim = None):
figure()
print "----------------------------------------------------------------"
for i, nc in enumerate([0, 1, 2, 5, 10]):
ncd = d(nc)
print ncd
ncd.summary(show_moments=True)
ncd.plot(label = "nonc=" + str(nc), color = colors[i%len(colors)])
print
if lim is not None:
xlim(lim[0], lim[1])
ylim(lim[2], lim[3])
title(titl)
legend()
show()
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.
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Noncentral T
| ... plot_nonc(lambda nc: NoncentralTDistr(2, nc), titl = "NoncentralT(2, nonc)")
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----------------------------------------------------------------
NoncentralTDistr(df=2,mu=0)#66364016
============= summary =============
NoncT(2,0)
mean = 0.0
var = inf
skewness = nan
kurtosis = nan
entropy = 1.9602792291600828
median = 0.0
mode = 6.1903394578241122e-09
medianad = 0.8164965809277253
iqrange(0.025) = 8.605305459498918
ci(0.05) = (-4.302652729749469, 4.3026527297494495)
range = (-inf, inf)
tailexp = (-3.0000000000004379, -3.0000000000004565)
int_err = -2.2204460492503131e-16
moments:
0 = 1.0000000000000002
1 = 0.0
2 = nan
3 = nan
4 = nan
5 = nan
6 = nan
7 = nan
8 = nan
9 = nan
10 = nan
NoncentralTDistr(df=2,mu=1)#66367376
============= summary =============
NoncT(2,1)
mean = 1.7724538509055168
var = inf
skewness = nan
kurtosis = nan
entropy = 2.032565640811077
median = 1.1424180717802386
mode = 0.75893851188818306
medianad = 0.9078066441827171
iqrange(0.025) = 10.103390219998012
ci(0.05) = (-1.4764994860084424, 8.626890733989569)
range = (-inf, inf)
tailexp = (-3.0000000000003451, -3.0000000000005218)
int_err = -4.4408920985006262e-16
moments:
0 = 1.0000000000000004
1 = 1.7724538509055168
2 = nan
3 = nan
4 = nan
5 = nan
6 = nan
7 = nan
8 = nan
9 = nan
10 = nan
NoncentralTDistr(df=2,mu=2)#66389264
============= summary =============
NoncT(2,2)
mean = 3.5449077018109922
var = inf
skewness = nan
kurtosis = nan
entropy = 2.2153700695930576
median = 2.3303902594719865
mode = 1.5468640851845601
medianad = 1.1550512381701201
iqrange(0.025) = 13.93583867865285
ci(0.05) = (0.04469873059773619, 13.980537409250585)
range = (-inf, inf)
tailexp = (-3.0000000000004099, -3.0000000000008575)
int_err = -1.3322676295501878e-15
moments:
0 = 1.0000000000000013
1 = 3.5449077018109922
2 = nan
3 = nan
4 = nan
5 = nan
6 = nan
7 = nan
8 = nan
9 = nan
10 = nan
NoncentralTDistr(df=2,mu=5)#66364336
============= summary =============
NoncT(2,5)
mean = 8.862269254527531
var = inf
skewness = nan
kurtosis = nan
entropy = 2.8425183550980853
median = 5.962374771525829
mode = 4.0126194901895431
medianad = 2.269713040233854
iqrange(0.025) = 29.758031070622845
ci(0.05) = (2.257334844081019, 32.015365914703864)
range = (-inf, inf)
tailexp = (-3.0000000000004845, -3.0000000000005218)
int_err = -1.1102230246251565e-15
moments:
0 = 1.0000000000000011
1 = 8.862269254527531
2 = nan
3 = nan
4 = nan
5 = nan
6 = nan
7 = nan
8 = nan
9 = nan
10 = nan
NoncentralTDistr(df=2,mu=10)#69383600
============= summary =============
NoncT(2,10)
mean = 17.724538509055037
var = inf
skewness = nan
kurtosis = nan
entropy = 3.4902865634157831
median = 11.988419035468151
mode = 8.1256617520309717
medianad = 4.355352575617786
iqrange(0.025) = 58.106197253538205
ci(0.05) = (5.038848593318069, 63.14504584685628)
range = (-inf, inf)
tailexp = (-10.24319552183813, -3.0000000000005591)
int_err = -1.5543122344752192e-15
moments:
0 = 1.0000000000000016
1 = 17.724538509055037
2 = nan
3 = nan
4 = nan
5 = nan
6 = nan
7 = nan
8 = nan
9 = nan
10 = nan
| ... plot_nonc(lambda nc: NoncentralTDistr(10, nc), titl = "NoncentralT(10, nonc)")
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----------------------------------------------------------------
NoncentralTDistr(df=10,mu=0)#70820816
============= summary =============
NoncT(10,0)
mean = -2.7755575615628914e-17
var = 1.2500000000000024
skewness = 1.58882185807825e-16
kurtosis = 3.9999999999999925
entropy = 1.5212624929756817
median = 0.0
mode = 6.0274295788821538e-09
medianad = 0.6998120613124307
iqrange(0.025) = 4.45627770397253
ci(0.05) = (-2.2281388519862757, 2.228138851986254)
range = (-inf, inf)
tailexp = (-11.000000000000284, -11.000000000000284)
int_err = -8.8817841970012523e-16
moments:
0 = 1.0000000000000009
1 = -2.7755575615628914e-17
2 = 1.2500000000000024
3 = 2.2204460492503131e-16
4 = 6.2500000000000124
5 = -1.4210854715202004e-14
6 = 78.125000000000398
7 = -1.6200374375330284e-12
8 = 2734.37500000006
9 = -1.837179297581315e-10
10 = nan
NoncentralTDistr(df=10,mu=1)#74379216
============= summary =============
NoncT(10,1)
mean = 1.0837223079391449
var = 1.3255459592750625
skewness = 0.39992972990584891
kurtosis = 4.2499413181413477
entropy = 1.5430433871472671
median = 1.025720922828001
mode = 0.93291034194131217
medianad = 0.7169797223557234
iqrange(0.025) = 4.575131194256144
ci(0.05) = (-1.0346256590795306, 3.540505535176614)
range = (-inf, inf)
tailexp = (-11.00000000000027, -11.00000000000027)
int_err = -8.8817841970012523e-16
moments:
0 = 1.0000000000000009
1 = 1.0837223079391449
2 = 2.5000000000000044
3 = 6.192698902509437
4 = 20.833333333333787
5 = 80.505085732622433
6 = 395.83333333333786
7 = 2394.5102423036828
8 = 19895.833333336261
9 = 270414.51874291606
10 = nan
NoncentralTDistr(df=10,mu=2)#74413200
============= summary =============
NoncT(10,2)
mean = 2.1674446158782885
var = 1.552183837100225
skewness = 0.72363329408286414
kurtosis = 4.8273295684844699
entropy = 1.6038742415428799
median = 2.053691151118488
mode = 1.8702078674151745
medianad = 0.7663524511650831
iqrange(0.025) = 4.916869970883092
ci(0.05) = (0.04096565549093609, 4.957835626374028)
range = (-inf, inf)
tailexp = (-11.000000000000307, -11.000000000000181)
int_err = -6.6613381477509392e-16
moments:
0 = 1.0000000000000007
1 = 2.1674446158782885
2 = 6.2500000000000071
3 = 21.674446158782899
4 = 89.583333333333456
5 = 439.68162207816738
6 = 2598.9583333333358
7 = 19094.154949403965
8 = 187317.70833333323
9 = 3012335.1694675167
10 = nan
NoncentralTDistr(df=10,mu=5)#103167568
============= summary =============
NoncT(10,5)
mean = 5.4186115396957231
var = 3.1386489818764018
skewness = 1.1915013284649849
kurtosis = 6.3154072187525401
entropy = 1.9063262108514267
median = 5.152684264812535
mode = 4.7155492907120564
medianad = 1.051562464702453
iqrange(0.025) = 6.877359219453013
ci(0.05) = (2.7556674169781727, 9.633026636431186)
range = (-inf, inf)
tailexp = (-11.000000000000433, -11.000000000000158)
int_err = -1.1102230246251565e-15
moments:
0 = 1.0000000000000011
1 = 5.4186115396957231
2 = 32.500000000000028
3 = 216.74446158782894
4 = 1620.8333333333344
5 = 13778.755058083421
6 = 136145.83333333372
7 = 1624551.3454249694
8 = 25259895.833333459
9 = 630530281.08540511
10 = nan
NoncentralTDistr(df=10,mu=10)#103839664
============= summary =============
NoncT(10,10)
mean = 10.837223079391444
var = 8.8045959275056056
skewness = 1.3621117864055567
kurtosis = 7.0845253856916131
entropy = 2.3966117728947571
median = 10.331273563114916
mode = 9.4949812759964338
medianad = 1.7250988211625042
iqrange(0.025) = 11.436240190750638
ci(0.05) = (6.5942102221556915, 18.03045041290633)
range = (-inf, inf)
tailexp = (-11.000000000000307, -11.000000000000732)
int_err = -8.8817841970012523e-16
moments:
0 = 1.0000000000000009
1 = 10.837223079391444
2 = 126.25000000000011
3 = 1594.6199673961703
4 = 22089.583333333372
5 = 341062.89205570531
6 = 6013098.9583333377
7 = 125980654.06495768
8 = 3389117317.7083015
9 = 144400264124.44336
10 = nan
| ... |
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Noncentral Chi square
| ... plot_nonc(lambda nc: NoncentralChiSquareDistr(2, nc), titl = "NoncentralChiSquare(2, nonc)")
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----------------------------------------------------------------
NoncentralChiSquare(df=2,lambda=0)#103169296
============= summary =============
NoncChi2(2,0)
mean = 2.0000000000000004
var = 4.000000000000008
skewness = 2.0000000000000089
kurtosis = 9.0000000000001403
entropy = 1.6931471805599465
median = 1.386294361119856
mode = 2.3674838630545864e-16
medianad = 0.9624236501191911
iqrange(0.025) = 7.327123292259132
ci(0.05) = (0.05063561596861359, 7.3777589082277455)
range = (0.0, inf)
tailexp = (None, -158.27198941847502)
int_err = 0.0
moments:
0 = 1.0
1 = 2.0000000000000004
2 = 8.0000000000000178
3 = 48.000000000000171
4 = 384.00000000000409
5 = 3840.0000000001064
6 = 46080.000000002772
7 = 645120.00000007404
8 = 10321920.000001989
9 = 185794560.00005379
10 = 3715891200.0014415
NoncentralChiSquare(df=2,lambda=1)#110306640
============= summary =============
NoncChi2(2,1)
mean = 3.0000000000000009
var = 8.0000000000000071
skewness = 1.767766952966364
kurtosis = 7.4999999999999449
entropy = 2.0966226994671597
median = 2.177038550303904
mode = 3.5366674438146647e-15
medianad = 1.4702116688484144
iqrange(0.025) = 10.390892489050817
ci(0.05) = (0.08330038643724205, 10.47419287548806)
range = (0.0, inf)
tailexp = (None, -149.68320312849369)
int_err = -4.4408920985006262e-16
moments:
0 = 1.0000000000000004
1 = 3.0000000000000009
2 = 17.0
3 = 139.00000000000006
4 = 1472.9999999999968
5 = 19090.999999999876
6 = 291792.99999999453
7 = 5129306.9999997923
8 = 101817088.99999154
9 = 2250495522.9996691
10 = 54780588560.986938
NoncentralChiSquare(df=2,lambda=2)#110391824
============= summary =============
NoncChi2(2,2)
mean = 4.0000000000000018
var = 12.000000000000007
skewness = 1.5396007178390005
kurtosis = 6.3333333333333242
entropy = 2.373050068002108
median = 3.0936118736811262
mode = 7.4666846728198261e-08
medianad = 1.955902214027441
iqrange(0.025) = 12.787395744436761
ci(0.05) = (0.13596528499266802, 12.92336102942943)
range = (0.0, inf)
tailexp = (None, -146.0193157967114)
int_err = -2.2204460492503131e-16
moments:
0 = 1.0000000000000002
1 = 4.0000000000000018
2 = 28.000000000000028
3 = 272.00000000000023
4 = 3344.0000000000055
5 = 49471.999999999985
6 = 852927.99999999895
7 = 16758015.999999948
8 = 369082623.9999975
9 = 8996922367.9999008
10 = 240294124543.99521
NoncentralChiSquare(df=2,lambda=5)#111076752
============= summary =============
NoncChi2(2,5)
mean = 7.0000000000000036
var = 24.000000000000018
skewness = 1.1567034896476116
kurtosis = 4.8333333333333277
entropy = 2.8540805687501845
median = 6.03441301933434
mode = 3.8440965130941214
medianad = 3.046829477549737
iqrange(0.025) = 18.458974498667118
ci(0.05) = (0.5147988393313607, 18.97377333799848)
range = (0.0, inf)
tailexp = (None, -138.75099491367538)
int_err = -6.6613381477509392e-16
moments:
0 = 1.0000000000000007
1 = 7.0000000000000036
2 = 73.000000000000071
3 = 983.00000000000091
4 = 16049.00000000002
5 = 306215.00000000041
6 = 6662905.000000013
7 = 162455095.00000036
8 = 4379998945.0000086
9 = 129231454535.00015
10 = 4137832886825.0093
NoncentralChiSquare(df=2,lambda=10)#111200048
============= summary =============
NoncChi2(2,10)
mean = 12.000000000000009
var = 44.000000000000014
skewness = 0.87712391149894509
kurtosis = 4.0413223140495829
entropy = 3.2337776610177489
median = 11.01687376621316
mode = 8.9405001408011078
medianad = 4.2874279598175296
iqrange(0.025) = 25.432208283076946
ci(0.05) = (2.0766291514586293, 27.508837434535575)
range = (0.0, inf)
tailexp = (None, -130.56040988872405)
int_err = -4.4408920985006262e-16
moments:
0 = 1.0000000000000004
1 = 12.000000000000009
2 = 188.00000000000017
3 = 3568.0000000000045
4 = 78864.000000000087
5 = 1979840.0000000023
6 = 55468479.999999933
7 = 1711768320.0000021
8 = 57598910720.000069
9 = 2096139381759.9973
10 = 81952643251199.859
| ... plot_nonc(lambda nc: NoncentralChiSquareDistr(10, nc), titl = "NoncentralChiSquare(10, nonc)")
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----------------------------------------------------------------
NoncentralChiSquare(df=10,lambda=0)#71971312
============= summary =============
NoncChi2(10,0)
mean = 10.000000000000004
var = 20.000000000000018
skewness = 0.89442719099991375
kurtosis = 4.1999999999999966
entropy = 2.8467303371806909
median = 9.341817765591962
mode = 8.0000001171460955
medianad = 2.8502164199062614
iqrange(0.025) = 17.236204570570507
ci(0.05) = (3.2469727802368404, 20.48317735080735)
range = (0.0, inf)
tailexp = (None, -154.27198941847513)
int_err = -4.4408920985006262e-16
moments:
0 = 1.0000000000000004
1 = 10.000000000000004
2 = 120.00000000000007
3 = 1680.0000000000014
4 = 26880.000000000022
5 = 483840.00000000058
6 = 9676800.0000000093
7 = 212889600.00000036
8 = 5109350400.0000067
9 = 132843110400.00034
10 = 3719607091200.0103
NoncentralChiSquare(df=10,lambda=1)#112548944
============= summary =============
NoncChi2(10,1)
mean = 11.000000000000005
var = 24.000000000000014
skewness = 0.88453796267170048
kurtosis = 4.1666666666666599
entropy = 2.9391754523214102
median = 10.285182180704636
mode = 8.8247439107194197
medianad = 3.127713808000056
iqrange(0.025) = 18.8832228163269
ci(0.05) = (3.5834431913885103, 22.46666600771541)
range = (0.0, inf)
tailexp = (None, -147.44346212041083)
int_err = 0.0
moments:
0 = 1.0
1 = 11.000000000000005
2 = 145.00000000000006
3 = 2227.0000000000023
4 = 39041.000000000029
5 = 769051.00000000093
6 = 16813201.000000015
7 = 403889795.0000006
8 = 10573236097.000015
9 = 299555470891.00055
10 = 9130832638481.0312
NoncentralChiSquare(df=10,lambda=2)#116677648
============= summary =============
NoncChi2(10,2)
mean = 11.999999999999996
var = 28.000000000000021
skewness = 0.86391879544966399
kurtosis = 4.1020408163265296
entropy = 3.0190346127763563
median = 11.243013356825138
mode = 9.6914192947246285
medianad = 3.390141606301141
iqrange(0.025) = 20.401965709952567
ci(0.05) = (3.943081665237083, 24.34504737518965)
range = (0.0, inf)
tailexp = (None, -143.85161004257196)
int_err = -4.4408920985006262e-16
moments:
0 = 1.0000000000000004
1 = 11.999999999999996
2 = 172.00000000000009
3 = 2864.0000000000023
4 = 54288.000000000022
5 = 1153472.0000000009
6 = 27139264.000000022
7 = 700180224.00000048
8 = 19648315648.000023
9 = 595656682496.00024
10 = 19396109036544.012
NoncentralChiSquare(df=10,lambda=5)#117379056
============= summary =============
NoncChi2(10,5)
mean = 15.0
var = 40.000000000000021
skewness = 0.79056941504209466
kurtosis = 3.8999999999999995
entropy = 3.207528555208282
median = 14.165927836310884
mode = 12.449641931119741
medianad = 4.096576949609718
iqrange(0.025) = 24.42243233310547
ci(0.05) = (5.152318702405864, 29.574751035511333)
range = (0.0, inf)
tailexp = (None, -136.64615094277852)
int_err = -4.4408920985006262e-16
moments:
0 = 1.0000000000000004
1 = 15.0
2 = 265.00000000000006
3 = 5375.0000000000009
4 = 122865.00000000006
5 = 3120815.0000000023
6 = 87112825.000000104
7 = 2648404575.0000033
8 = 87050646625.000137
9 = 3074393034575.0039
10 = 116054342142825.11
NoncentralChiSquare(df=10,lambda=10)#117522960
============= summary =============
NoncChi2(10,10)
mean = 20.000000000000021
var = 60.000000000000043
skewness = 0.68853037265908923
kurtosis = 3.6666666666666572
entropy = 3.4238121816625759
median = 19.107384707413736
mode = 17.276879326635655
medianad = 5.077420399226437
iqrange(0.025) = 29.996990768000746
ci(0.05) = (7.5338697787430435, 37.53086054674379)
range = (0.0, inf)
tailexp = (None, -128.48675401585879)
int_err = -6.6613381477509392e-16
moments:
0 = 1.0000000000000007
1 = 20.000000000000021
2 = 460.00000000000034
3 = 11920.000000000007
4 = 342800.00000000023
5 = 10815040.000000013
6 = 370897600.0000003
7 = 13723884800.000017
8 = 544510009600.00073
9 = 23044548736000.031
10 = 1035664044723202.1
| ... |
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Noncentral Beta
| ... plot_nonc(lambda nc: NoncentralBetaDistr(1, 1, nc), titl = "NoncentralBeta(1, 1, nonc)")
|
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----------------------------------------------------------------
NoncentralBetaDistr(alpha=1,beta=1,lambda=0)#112442960
============= summary =============
NoncBeta(1,1,0)
mean = 0.50000000000000011
var = 0.083333333333333356
skewness = -1.9469997199633577e-15
kurtosis = 1.8000000000000005
entropy = -2.2508739996880788e-15
median = 0.5
mode = 0.026229840838391288
medianad = 0.25
iqrange(0.025) = 0.9499999999999982
ci(0.05) = (0.02499999999999954, 0.9749999999999978)
range = (0.0, 1.0)
tailexp = (None, None)
int_err = -2.2204460492503131e-15
moments:
0 = 1.0000000000000022
1 = 0.50000000000000011
2 = 0.33333333333333337
3 = 0.25
4 = 0.20000000000000004
5 = 0.16666666666666666
6 = 0.14285714285714285
7 = 0.125
8 = 0.11111111111111112
9 = 0.099999999999999992
10 = 0.090909090909090912
NoncentralBetaDistr(alpha=1,beta=1,lambda=1)#133318960
============= summary =============
NoncBeta(1,1,1)
mean = 0.5738773611494663
var = 0.079645885164394456
skewness = -0.30915299924560946
kurtosis = 1.9382346129962285
entropy = -0.032981926300903498
median = 0.6082020162263387
mode = 0.99999997067098545
medianad = 0.23187077199719475
iqrange(0.025) = 0.9428225179076408
ci(0.05) = (0.040393903618925676, 0.9832164215265665)
range = (0.0, 1.0)
tailexp = (None, None)
int_err = 2.3314683517128287e-15
moments:
0 = 0.99999999999999767
1 = 0.5738773611494663
2 = 0.40898111080426958
3 = 0.31917000276157415
4 = 0.26218663720987745
5 = 0.22266703487653369
6 = 0.19359469777791613
7 = 0.17128660296070614
8 = 0.15361640300423257
9 = 0.13926783916429222
10 = 0.12738135190461969
NoncentralBetaDistr(alpha=1,beta=1,lambda=2)#134034544
============= summary =============
NoncBeta(1,1,2)
mean = 0.63212055882855778
var = 0.071941363792041246
skewness = -0.56163072472903064
kurtosis = 2.258770980059611
entropy = -0.107153583906737
median = 0.6850769421544973
mode = 0.99999997720537714
medianad = 0.20033790278970495
iqrange(0.025) = 0.9236218543023521
ci(0.05) = (0.06375938805553971, 0.9873812423578918)
range = (0.0, 1.0)
tailexp = (None, None)
int_err = -2.2204460492503131e-16
moments:
0 = 1.0000000000000002
1 = 0.63212055882855778
2 = 0.47151776468576934
3 = 0.37817005891403821
4 = 0.31642635245846296
5 = 0.27233529713460702
6 = 0.23918586063082928
7 = 0.21331547151489411
8 = 0.19254426043525386
9 = 0.17548936309305485
10 = 0.16122929896605837
NoncentralBetaDistr(alpha=1,beta=1,lambda=5)#135477008
============= summary =============
NoncBeta(1,1,5)
mean = 0.74686640022017636
var = 0.04720433986987408
skewness = -1.1115465368283606
kurtosis = 3.6674999319064203
entropy = -0.39807563031623217
median = 0.8080123179913834
mode = 0.9999999753426333
medianad = 0.1299478410662351
iqrange(0.025) = 0.8031790798721575
ci(0.05) = (0.18959475647046786, 0.9927738363426254)
range = (0.0, 1.0)
tailexp = (None, None)
int_err = -8.8817841970012523e-16
moments:
0 = 1.0000000000000009
1 = 0.74686640022017636
2 = 0.60501375964771809
3 = 0.51097523263410749
4 = 0.44325283704723756
5 = 0.3918679073819063
6 = 0.35142042674010981
7 = 0.31869327264897468
8 = 0.29163603145517836
9 = 0.26887407260652779
10 = 0.24944856619321057
NoncentralBetaDistr(alpha=1,beta=1,lambda=10)#135687984
============= summary =============
NoncBeta(1,1,10)
mean = 0.83973048212003665
var = 0.023068331702421587
skewness = -1.6100974829039867
kurtosis = 6.0198255036441068
entropy = -0.83344942576190806
median = 0.885655915984701
mode = 0.99999997355462433
medianad = 0.07876427304530455
iqrange(0.025) = 0.5650867645824653
ci(0.05) = (0.4306950876671735, 0.9957818522496389)
range = (0.0, 1.0)
tailexp = (None, None)
int_err = 1.1102230246251565e-16
moments:
0 = 0.99999999999999989
1 = 0.83973048212003665
2 = 0.72821561430397064
3 = 0.64460594712642671
4 = 0.57908698973181205
5 = 0.52614126283523532
6 = 0.48235658151726157
7 = 0.4454842501884731
8 = 0.41397165679822101
9 = 0.38670739498360301
10 = 0.36287245559199377
| ... plot_nonc(lambda nc: NoncentralBetaDistr(10, 15, nc), titl = "NoncentralBeta(10, 15, nonc)")
|
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.
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----------------------------------------------------------------
NoncentralBetaDistr(alpha=10,beta=15,lambda=0)#134036816
============= summary =============
NoncBeta(10,15,0)
mean = 0.39999999999999836
var = 0.00923076923076919
skewness = 0.15419748144198747
kurtosis = 2.820105820105844
entropy = -0.92722950454835984
median = 0.3972924046348387
mode = 0.39130434780072687
medianad = 0.06631350575912001
iqrange(0.025) = 0.37296671064538495
ci(0.05) = (0.22109690534667853, 0.5940636159920635)
range = (0.0, 1.0)
tailexp = (None, None)
int_err = 4.3298697960381105e-15
moments:
0 = 0.99999999999999567
1 = 0.39999999999999836
2 = 0.16923076923076849
3 = 0.075213675213674891
4 = 0.034920634920634776
5 = 0.016858237547892646
6 = 0.0084291187739463213
7 = 0.0043505129155851996
8 = 0.0023112099864046371
9 = 0.0012606599925843475
10 = 0.00070448646644419429
NoncentralBetaDistr(alpha=10,beta=15,lambda=1)#72005648
============= summary =============
NoncBeta(10,15,1)
mean = 0.41132853724592888
var = 0.0093795162593731645
skewness = 0.12864812766286643
kurtosis = 2.8070566164177673
entropy = -0.91855904303181013
median = 0.4090578635207688
mode = 0.40405298675856804
medianad = 0.06690932478187445
iqrange(0.025) = 0.3759629514866686
ci(0.05) = (0.2297162391702446, 0.6056791906569132)
range = (0.0, 1.0)
tailexp = (None, None)
int_err = 5.1070259132757201e-15
moments:
0 = 0.99999999999999489
1 = 0.41132853724592888
2 = 0.17857068181225003
3 = 0.081284204970535373
4 = 0.038586465012870844
5 = 0.019017334009519087
6 = 0.0096941826394799421
7 = 0.0050947784580311854
8 = 0.0027529252539922515
9 = 0.0015257434387586741
10 = 0.00086552950784239799
NoncentralBetaDistr(alpha=10,beta=15,lambda=2)#142203120
============= summary =============
NoncBeta(10,15,2)
mean = 0.42225172865424165
var = 0.0094878147916762461
skewness = 0.1039350234394301
kurtosis = 2.7974452686351667
entropy = -0.9122674656662545
median = 0.4204167343547491
mode = 0.41639828611991553
medianad = 0.0673382053680876
iqrange(0.025) = 0.378147840257382
ci(0.05) = (0.23834053259134957, 0.6164883728487316)
range = (0.0, 1.0)
tailexp = (None, None)
int_err = 4.5519144009631418e-15
moments:
0 = 0.99999999999999545
1 = 0.42225172865424165
2 = 0.18778433714317228
3 = 0.087400806429204281
4 = 0.042353572650929802
5 = 0.02127720431828891
6 = 0.01104122269775816
7 = 0.0059001256086713728
8 = 0.0032381677871350292
9 = 0.0018211176826589141
10 = 0.0010473955532219672
NoncentralBetaDistr(alpha=10,beta=15,lambda=5)#144016080
============= summary =============
NoncBeta(10,15,5)
mean = 0.45278943439597108
var = 0.0096201432000261478
skewness = 0.035894349843292657
kurtosis = 2.7855490537516658
entropy = -0.90437091305234962
median = 0.4521888959049869
mode = 0.45096865852796064
medianad = 0.06783891429956715
iqrange(0.025) = 0.38090865641889937
ci(0.05) = (0.2640769200434825, 0.6449855764623819)
range = (0.0, 1.0)
tailexp = (None, None)
int_err = 4.4408920985006262e-15
moments:
0 = 0.99999999999999556
1 = 0.45278943439597108
2 = 0.21463841510065051
3 = 0.10593167365957094
4 = 0.054185458799116799
5 = 0.028618296939051144
6 = 0.015557300575710158
7 = 0.008681302069808652
8 = 0.0049612527290364876
9 = 0.0028979013394721189
10 = 0.0017270384300759722
NoncentralBetaDistr(alpha=10,beta=15,lambda=10)#144813328
============= summary =============
NoncBeta(10,15,10)
mean = 0.49726921410214625
var = 0.0094172031042719512
skewness = -0.057326363642821752
kurtosis = 2.8021279892218276
entropy = -0.91504528557671549
median = 0.4983456657864689
mode = 0.50086299019577196
medianad = 0.06697638936506115
iqrange(0.025) = 0.3771702486843422
ci(0.05) = (0.30575323304508756, 0.6829234817294297)
range = (0.0, 1.0)
tailexp = (None, None)
int_err = 2.9976021664879227e-15
moments:
0 = 0.999999999999997
1 = 0.49726921410214625
2 = 0.25669387439803881
3 = 0.13695934289897821
4 = 0.075261978029826301
5 = 0.04246970667067592
6 = 0.024547891178927757
7 = 0.014502755788461604
8 = 0.0087415029790017529
9 = 0.0053668936584482753
10 = 0.0033515783484655798
| ... |
||
|
.
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Noncentral F
| ... plot_nonc(lambda nc: NoncentralFDistr(1, 1, nc), titl = "NoncentralF(1, 1, nonc)", lim = [-0.1, 3, 0, 0.9])
|
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|
.
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----------------------------------------------------------------
NoncentralFDistr(df1=1,df2=1,lambda=0)#142219664
============= summary =============
NoncF(1,1,0)
mean = nan
var = nan
skewness = nan
kurtosis = nan
entropy = 2.5310242469692885
median = 0.9999999999999971
mode = 6.5449953952479743e-17
medianad = 0.9717365435132885
iqrange(0.025) = 647.7874677654179
ci(0.05) = (0.0015437125086741295, 647.7890114779266)
range = (0.0, inf)
tailexp = (None, -1.5000000000003169)
int_err = 1.3322676295501878e-15
moments:
0 = 0.99999999999999867
1 = nan
2 = nan
3 = nan
4 = nan
5 = nan
6 = nan
7 = nan
8 = nan
9 = nan
10 = nan
NoncentralFDistr(df1=1,df2=1,lambda=1)#134051600
============= summary =============
NoncF(1,1,1)
mean = nan
var = nan
skewness = nan
kurtosis = nan
entropy = 3.3555913521807286
median = 2.2954203805980216
mode = 6.1802553028065065e-17
medianad = 2.2143875871903624
iqrange(0.025) = 1385.1322785585317
ci(0.05) = (0.0041919517836761355, 1385.1364705103153)
range = (0.0, inf)
tailexp = (None, -1.5000000000003169)
int_err = 3.3306690738754696e-15
moments:
0 = 0.99999999999999667
1 = nan
2 = nan
3 = nan
4 = nan
5 = nan
6 = nan
7 = nan
8 = nan
9 = nan
10 = nan
NoncentralFDistr(df1=1,df2=1,lambda=2)#159446416
============= summary =============
NoncF(1,1,2)
mean = nan
var = nan
skewness = nan
kurtosis = nan
entropy = 3.9265356549232493
median = 4.0069613933821495
mode = 4.3634370272011962e-17
medianad = 3.796203261948913
iqrange(0.025) = 2245.4715097329276
ci(0.05) = (0.011310370509324203, 2245.482820103437)
range = (0.0, inf)
tailexp = (None, -1.5000000000003542)
int_err = 6.2172489379008766e-15
moments:
0 = 0.99999999999999378
1 = nan
2 = nan
3 = nan
4 = nan
5 = nan
6 = nan
7 = nan
8 = nan
9 = nan
10 = nan
NoncentralFDistr(df1=1,df2=1,lambda=5)#159698704
============= summary =============
NoncF(1,1,5)
mean = nan
var = nan
skewness = nan
kurtosis = nan
entropy = 4.8939846800934692
median = 10.103710479505944
mode = 6.1802553028065065e-17
medianad = 9.005575569013857
iqrange(0.025) = 5130.382205818015
ci(0.05) = (0.15750742797489098, 5130.539713245989)
range = (0.0, inf)
tailexp = (None, -1.5000000000002889)
int_err = 8.992806499463768e-15
moments:
0 = 0.99999999999999101
1 = nan
2 = nan
3 = nan
4 = nan
5 = nan
6 = nan
7 = nan
8 = nan
9 = nan
10 = nan
NoncentralFDistr(df1=1,df2=1,lambda=10)#159445168
============= summary =============
NoncF(1,1,10)
mean = nan
var = nan
skewness = nan
kurtosis = nan
entropy = 5.6232262399564013
median = 20.9886788068141
mode = 2.3289887644643477
medianad = 17.922712518472153
iqrange(0.025) = 10183.32765475939
ci(0.05) = (0.9992904727604669, 10184.326945232151)
range = (0.0, inf)
tailexp = (None, -1.5000000000004288)
int_err = 1.0436096431476471e-14
moments:
0 = 0.99999999999998956
1 = nan
2 = nan
3 = nan
4 = nan
5 = nan
6 = nan
7 = nan
8 = nan
9 = nan
10 = nan
| ... plot_nonc(lambda nc: NoncentralFDistr(10, 20, nc), titl = "NoncentralF(10, 20, nonc)")
|
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|
.
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----------------------------------------------------------------
NoncentralFDistr(df1=10,df2=20,lambda=0)#159698864
============= summary =============
NoncF(10,20,0)
mean = 1.1111111111111134
var = 0.43209876543209946
skewness = 1.8351920959819077
kurtosis = 9.8938775510203705
entropy = 0.80325807970145024
median = 0.9662638885929155
mode = 0.72727273810629056
medianad = 0.353645635124445
iqrange(0.025) = 2.481149137215127
ci(0.05) = (0.2925222379839803, 2.7736713751991076)
range = (0.0, inf)
tailexp = (None, -10.999999999975055)
int_err = -1.3322676295501878e-15
moments:
0 = 1.0000000000000013
1 = 1.1111111111111134
2 = 1.6666666666666692
3 = 3.3333333333333384
4 = 8.888888888888907
5 = 32.000000000000057
6 = 160.00000000000011
7 = 1173.3333333333323
8 = 14079.999999999984
9 = 366079.99999650108
10 = nan
NoncentralFDistr(df1=10,df2=20,lambda=1)#161274512
============= summary =============
NoncF(10,20,1)
mean = 1.2222222222222237
var = 0.52006172839506259
skewness = 1.8290356529428318
kurtosis = 9.8495238262956342
entropy = 0.89702211712671687
median = 1.0636917860814479
mode = 0.80194845221286826
medianad = 0.3884517638346881
iqrange(0.025) = 2.7226106260908765
ci(0.05) = (0.322758535801714, 3.0453691618925904)
range = (0.0, inf)
tailexp = (None, -10.999999999972818)
int_err = -1.5543122344752192e-15
moments:
0 = 1.0000000000000016
1 = 1.2222222222222237
2 = 2.0138888888888924
3 = 4.4186507936508033
4 = 12.910383597883627
5 = 50.863161375661498
6 = 277.99604828042396
7 = 2226.0240024250497
8 = 29137.004235560016
9 = 825494.57365605189
10 = nan
NoncentralFDistr(df1=10,df2=20,lambda=2)#163462832
============= summary =============
NoncF(10,20,2)
mean = 1.333333333333335
var = 0.61111111111111194
skewness = 1.8163593497309056
kurtosis = 9.7615112160566468
entropy = 0.98012006444187583
median = 1.1624039266221915
mode = 0.8799399266304766
medianad = 0.42214839581726177
iqrange(0.025) = 2.9528138350825057
ci(0.05) = (0.3549071583894989, 3.3077209934720044)
range = (0.0, inf)
tailexp = (None, -10.999999999971179)
int_err = -1.9984014443252818e-15
moments:
0 = 1.000000000000002
1 = 1.333333333333335
2 = 2.3888888888888928
3 = 5.6825396825396908
4 = 17.952380952380985
5 = 76.287830687830834
6 = 448.73121693121772
7 = 3859.0179894179923
8 = 54145.490652557295
9 = 1641470.1347297181
10 = nan
NoncentralFDistr(df1=10,df2=20,lambda=5)#161254928
============= summary =============
NoncF(10,20,5)
mean = 1.6666666666666692
var = 0.90277777777777923
skewness = 1.7733920390383775
kurtosis = 9.4803043110735157
entropy = 1.1840938773902951
median = 1.4631480545186373
mode = 1.1268311177888968
medianad = 0.5173410948529611
iqrange(0.025) = 3.5960479107177648
ci(0.05) = (0.46178063112227075, 4.057828541840036)
range = (0.0, inf)
tailexp = (None, -10.999999999966779)
int_err = -1.3322676295501878e-15
moments:
0 = 1.0000000000000013
1 = 1.6666666666666692
2 = 3.6805555555555607
3 = 10.664682539682554
4 = 40.629960317460394
5 = 206.40310846560888
6 = 1440.3575562169344
7 = 14596.586061507967
8 = 239888.24576995178
9 = 8472203.0272725429
10 = nan
NoncentralFDistr(df1=10,df2=20,lambda=10)#164504272
============= summary =============
NoncF(10,20,10)
mean = 2.2222222222222259
var = 1.4506172839506197
skewness = 1.7205627636672378
kurtosis = 9.1581193817499535
entropy = 1.4327902005604325
median = 1.9714893737454442
mode = 1.5586834473942461
medianad = 0.6619112343407831
iqrange(0.025) = 4.571299599008926
ci(0.05) = (0.6676701063045128, 5.238969705313439)
range = (0.0, inf)
tailexp = (None, -10.999999999960592)
int_err = -1.3322676295501878e-15
moments:
0 = 1.0000000000000013
1 = 2.2222222222222259
2 = 6.3888888888888982
3 = 23.650793650793698
4 = 113.3597883597886
5 = 715.28042328042511
6 = 6132.5661375661603
7 = 75638.694885362012
8 = 1500523.6155202929
9 = 63504598.5883056
10 = nan
| ... show()
|
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|
.
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