ROOT   Reference Guide
Searching...
No Matches
TestBinomial.C File Reference

## Detailed Description

Perform a fit to a set of data with binomial errors like those derived from the division of two histograms.

Three different fits are performed and compared:

• simple least square fit to the divided histogram obtained from TH1::Divide with option b
• least square fit to the TGraphAsymmErrors obtained from TGraphAsymmErrors::BayesDivide
• likelihood fit performed on the dividing histograms using binomial statistics with the TBinomialEfficiency class

The first two methods are biased while the last one is statistical correct. Running the script passing an integer value n larger than 1, n fits are performed and the bias are also shown. To run the script :

to show the bias performing 100 fits for 1000 events per "experiment"

root[0]: .x TestBinomial.C+

to show the bias performing 100 fits for 1000 events per "experiment"

.x TestBinomial.C+(100, 1000)
32 68
****************************************
Chi2 = 0.350714
NDf = 3
Edm = 1.27001e-06
NCalls = 81
p0 = 0.694132 +/- 0.210029
p1 = 19.3471 +/- 5.85483
p2 = 5.2245 +/- 5.11013
****************************************
MinFCN = 14.3081
Chi2 = 28.6162
NDf = 21
Edm = 4.11934e-08
NCalls = 91
p0 = 0.822966 +/- 0.0807557 (limited)
p1 = 21.9819 +/- 2.14579
p2 = 3.36105 +/- 1.05866
****************************************
Chi2 = 1.64738
NDf = 5
Edm = 1.01171e-06
NCalls = 137
p0 = 0.677329 +/- 0.135567 (limited)
p1 = 15.5028 +/- 4.11118
p2 = 4.10441 +/- 2.77044
****************************************
MinFCN = 19.363
Chi2 = 38.7261
NDf = 25
Edm = 9.40378e-08
NCalls = 80
p0 = 0.778188 +/- 0.0815568 (limited)
p1 = 23.7948 +/- 2.21356
p2 = 4.58769 +/- 1.24153
****************************************
Chi2 = 0.928456
NDf = 6
Edm = 1.46917e-08
NCalls = 75
p0 = 0.578806 +/- 0.128412 (limited)
p1 = 19.8914 +/- 2.83678
p2 = 3.39323 +/- 1.96156
****************************************
MinFCN = 11.7144
Chi2 = 23.4287
NDf = 23
Edm = 7.44806e-08
NCalls = 73
p0 = 0.740898 +/- 0.079731 (limited)
p1 = 21.5953 +/- 2.12198
p2 = 2.98575 +/- 1.16957
****************************************
Chi2 = 2.56551
NDf = 7
Edm = 1.19556e-08
NCalls = 109
p0 = 0.57261 +/- 0.16552 (limited)
p1 = 21.4104 +/- 5.10611
p2 = 5.58786 +/- 3.30889
****************************************
MinFCN = 12.7185
Chi2 = 25.4369
NDf = 23
Edm = 7.33141e-08
NCalls = 74
p0 = 0.861581 +/- 0.082929 (limited)
p1 = 28.1952 +/- 3.60519
p2 = 7.31775 +/- 2.14695
****************************************
Chi2 = 7.37095
NDf = 10
Edm = 1.54804e-06
NCalls = 87
p0 = 0.667689 +/- 0.152841 (limited)
p1 = 24.0146 +/- 2.40617
p2 = 3.63777 +/- 1.74672
****************************************
MinFCN = 9.05615
Chi2 = 18.1123
NDf = 23
Edm = 2.30749e-07
NCalls = 71
p0 = 0.842186 +/- 0.0921999 (limited)
p1 = 26.3581 +/- 2.99562
p2 = 5.28694 +/- 1.78724
****************************************
Chi2 = 0.747776
NDf = 6
Edm = 2.75121e-06
NCalls = 76
p0 = 0.651877 +/- 0.155245 (limited)
p1 = 18.9865 +/- 2.68321
p2 = 2.68989 +/- 1.28756
****************************************
MinFCN = 15.9733
Chi2 = 31.9466
NDf = 26
Edm = 5.1941e-07
NCalls = 62
p0 = 0.794215 +/- 0.0873938 (limited)
p1 = 25.0012 +/- 3.13976
p2 = 5.16842 +/- 1.65839
****************************************
Chi2 = 0.433039
NDf = 4
Edm = 3.07902e-07
NCalls = 104
p0 = 0.500967 +/- 0.254652 (limited)
p1 = 19.4199 +/- 9.30614
p2 = 6.46947 +/- 8.16624
****************************************
MinFCN = 17.807
Chi2 = 35.614
NDf = 24
Edm = 5.43825e-09
NCalls = 98
p0 = 0.748311 +/- 0.0866402 (limited)
p1 = 22.4098 +/- 2.06254
p2 = 3.36062 +/- 0.902421
****************************************
Chi2 = 4.49197
NDf = 9
Edm = 4.04441e-06
NCalls = 113
p0 = 0.623236 +/- 0.107197 (limited)
p1 = 20.8129 +/- 1.0507
p2 = 1.22179 +/- 1.09027
****************************************
MinFCN = 10.5454
Chi2 = 21.0907
NDf = 22
Edm = 1.84998e-08
NCalls = 101
p0 = 0.7513 +/- 0.0923543 (limited)
p1 = 23.3695 +/- 3.23382
p2 = 3.90837 +/- 1.83804
****************************************
Chi2 = 2.54966
NDf = 6
Edm = 1.48922e-07
NCalls = 93
p0 = 0.382687 +/- 0.226798 (limited)
p1 = 18.0539 +/- 6.38962
p2 = 3.0464 +/- 5.58751
****************************************
MinFCN = 7.09023
Chi2 = 14.1805
NDf = 22
Edm = 1.88451e-08
NCalls = 149
p0 = 1 +/- 0.132534 (limited)
p1 = 29.3106 +/- 2.29361
p2 = 6.14658 +/- 1.45195
****************************************
Chi2 = 1.46531
NDf = 7
Edm = 2.36369e-06
NCalls = 90
p0 = 0.575891 +/- 0.187613 (limited)
p1 = 17.6126 +/- 7.68638
p2 = 2.99185 +/- 6.18408
****************************************
MinFCN = 15.9432
Chi2 = 31.8864
NDf = 23
Edm = 9.70221e-07
NCalls = 76
p0 = 0.765903 +/- 0.0805873 (limited)
p1 = 23.9216 +/- 2.50269
p2 = 4.42272 +/- 1.34342
****************************************
Chi2 = 3.31728
NDf = 6
Edm = 8.18927e-07
NCalls = 64
p0 = 0.59853 +/- 0.124912 (limited)
p1 = 17.9048 +/- 3.49062
p2 = 3.52241 +/- 2.09942
****************************************
MinFCN = 21.6362
Chi2 = 43.2724
NDf = 26
Edm = 2.82218e-06
NCalls = 80
p0 = 0.64315 +/- 0.0777258 (limited)
p1 = 19.2211 +/- 1.75093
p2 = 2.29991 +/- 0.890814
****************************************
Chi2 = 0.413866
NDf = 6
Edm = 5.34616e-09
NCalls = 82
p0 = 0.654352 +/- 0.198145 (limited)
p1 = 20.6178 +/- 3.66715
p2 = 4.03019 +/- 2.20627
****************************************
MinFCN = 9.09822
Chi2 = 18.1964
NDf = 19
Edm = 2.73834e-07
NCalls = 71
p0 = 0.809718 +/- 0.0969513 (limited)
p1 = 22.5716 +/- 2.36934
p2 = 3.95798 +/- 1.33784
****************************************
Chi2 = 1.21002
NDf = 4
Edm = 2.90565e-08
NCalls = 82
p0 = 0.651685 +/- 0.159188 (limited)
p1 = 19.3369 +/- 2.66645
p2 = 2.81842 +/- 2.20413
****************************************
MinFCN = 16.871
Chi2 = 33.7421
NDf = 24
Edm = 9.78264e-08
NCalls = 73
p0 = 0.780957 +/- 0.0794324 (limited)
p1 = 22.7262 +/- 1.91125
p2 = 2.78007 +/- 0.877452
****************************************
Chi2 = 0.752979
NDf = 7
Edm = 5.34806e-06
NCalls = 101
p0 = 0.643852 +/- 0.170146 (limited)
p1 = 21.01 +/- 4.32394
p2 = 5.36976 +/- 3.12567
****************************************
MinFCN = 12.9202
Chi2 = 25.8404
NDf = 23
Edm = 1.28006e-08
NCalls = 100
p0 = 0.794265 +/- 0.0958159 (limited)
p1 = 24.1679 +/- 3.59479
p2 = 4.72785 +/- 2.02176
****************************************
Chi2 = 2.5161
NDf = 8
Edm = 6.68524e-10
NCalls = 61
p0 = 0.628793 +/- 0.103749 (limited)
p1 = 17.4724 +/- 2.12101
p2 = 2.59351 +/- 1.42575
****************************************
MinFCN = 17.7487
Chi2 = 35.4974
NDf = 24
Edm = 4.85421e-08
NCalls = 84
p0 = 0.739601 +/- 0.111147 (limited)
p1 = 23.7592 +/- 3.70376
p2 = 4.88756 +/- 1.97092
****************************************
Chi2 = 1.27043
NDf = 8
Edm = 6.23845e-06
NCalls = 72
p0 = 0.561127 +/- 0.138134 (limited)
p1 = 18.1601 +/- 3.22498
p2 = 3.50338 +/- 1.84312
****************************************
MinFCN = 10.3177
Chi2 = 20.6353
NDf = 25
Edm = 4.17867e-06
NCalls = 74
p0 = 0.803115 +/- 0.0973933 (limited)
p1 = 24.5223 +/- 3.6204
p2 = 6.04914 +/- 2.15838
****************************************
Chi2 = 2.84972
NDf = 8
Edm = 1.39524e-06
NCalls = 90
p0 = 0.693419 +/- 0.285373 (limited)
p1 = 24.7834 +/- 7.96871
p2 = 5.95505 +/- 3.88805
****************************************
MinFCN = 14.2763
Chi2 = 28.5526
NDf = 27
Edm = 1.16259e-07
NCalls = 71
p0 = 0.81816 +/- 0.0960388 (limited)
p1 = 27.5551 +/- 3.48223
p2 = 5.91219 +/- 1.84521
****************************************
Chi2 = 3.67016
NDf = 5
Edm = 1.80141e-06
NCalls = 82
p0 = 0.502645 +/- 0.176121 (limited)
p1 = 20.1539 +/- 2.79976
p2 = 2.70329 +/- 1.65981
****************************************
MinFCN = 9.70246
Chi2 = 19.4049
NDf = 21
Edm = 4.83549e-06
NCalls = 68
p0 = 0.862268 +/- 0.0732858 (limited)
p1 = 22.9201 +/- 1.83831
p2 = 2.68862 +/- 0.964839
****************************************
Invalid FitResult (status = 3 )
****************************************
Chi2 = 0.936088
NDf = 1
Edm = 0.106873
NCalls = 83
p0 = 0.41816 +/- 0.669497 (limited)
p1 = 18.3049 +/- 3.25491
p2 = 3.06774 +/- 40.715
****************************************
Chi2 = 3.77203
NDf = 8
Edm = 1.56279e-05
NCalls = 84
p0 = 0.642277 +/- 0.195607 (limited)
p1 = 22.9222 +/- 4.97062
p2 = 5.05681 +/- 2.69739
****************************************
MinFCN = 16.8304
Chi2 = 33.6608
NDf = 24
Edm = 5.58496e-07
NCalls = 72
p0 = 0.62357 +/- 0.0902387 (limited)
p1 = 20.2778 +/- 2.24768
p2 = 2.93813 +/- 1.24803
****************************************
Chi2 = 0.47406
NDf = 6
Edm = 1.7448e-06
NCalls = 88
p0 = 0.635811 +/- 0.173792 (limited)
p1 = 21.0478 +/- 3.90109
p2 = 3.91609 +/- 2.85302
****************************************
MinFCN = 10.7469
Chi2 = 21.4938
NDf = 21
Edm = 2.82067e-07
NCalls = 90
p0 = 0.761502 +/- 0.0976432 (limited)
p1 = 23.1813 +/- 2.58651
p2 = 3.04135 +/- 1.22248
****************************************
Chi2 = 2.39556
NDf = 8
Edm = 4.51695e-08
NCalls = 81
p0 = 0.564008 +/- 0.188334 (limited)
p1 = 19.2305 +/- 5.64705
p2 = 4.00431 +/- 3.2294
****************************************
MinFCN = 16.5802
Chi2 = 33.1604
NDf = 27
Edm = 2.38499e-09
NCalls = 73
p0 = 0.670525 +/- 0.116925 (limited)
p1 = 23.7189 +/- 4.27475
p2 = 5.77511 +/- 2.44309
****************************************
Chi2 = 2.71864
NDf = 3
Edm = 2.02651e-07
NCalls = 84
p0 = 0.430955 +/- 0.103386 (limited)
p1 = 15.3556 +/- 1.58614
p2 = 1.18646 +/- 1.05279
****************************************
MinFCN = 14.442
Chi2 = 28.884
NDf = 25
Edm = 8.50827e-07
NCalls = 110
p0 = 0.931083 +/- 0.142888 (limited)
p1 = 27.3321 +/- 5.16548
p2 = 5.43478 +/- 2.66681
****************************************
Chi2 = 3.91497
NDf = 3
Edm = 9.71484e-06
NCalls = 172
p0 = 0.999991 +/- 0.973989 (limited)
p1 = 26.3679 +/- 4.16357
p2 = 10.2085 +/- 7.97289
****************************************
MinFCN = 13.7743
Chi2 = 27.5485
NDf = 26
Edm = 4.38758e-07
NCalls = 97
p0 = 0.94497 +/- 0.0525858 (limited)
p1 = 28.5699 +/- 2.31631
p2 = 4.52203 +/- 1.14841
****************************************
Chi2 = 3.69474
NDf = 4
Edm = 1.0286e-07
NCalls = 124
p0 = 0.566565 +/- 0.300627 (limited)
p1 = 22.9958 +/- 7.83199
p2 = 6.59909 +/- 5.25595
****************************************
MinFCN = 12.1694
Chi2 = 24.3388
NDf = 24
Edm = 1.18132e-06
NCalls = 93
p0 = 0.902749 +/- 0.0643623 (limited)
p1 = 23.1006 +/- 1.54526
p2 = 3.46387 +/- 0.844882
****************************************
Chi2 = 1.01429
NDf = 10
Edm = 2.60252e-06
NCalls = 94
p0 = 0.610818 +/- 0.175926 (limited)
p1 = 23.3058 +/- 5.77903
p2 = 5.09666 +/- 2.59915
****************************************
MinFCN = 7.14727
Chi2 = 14.2945
NDf = 19
Edm = 1.36278e-07
NCalls = 95
p0 = 0.900785 +/- 0.229879 (limited)
p1 = 28.3188 +/- 10.6921
p2 = 6.84773 +/- 5.79821
****************************************
Chi2 = 3.63097
NDf = 7
Edm = 2.77767e-07
NCalls = 123
p0 = 0.643028 +/- 0.225348 (limited)
p1 = 21.4306 +/- 4.46994
p2 = 3.95327 +/- 2.04398
****************************************
MinFCN = 13.9433
Chi2 = 27.8865
NDf = 21
Edm = 3.43187e-07
NCalls = 63
p0 = 0.683396 +/- 0.104286 (limited)
p1 = 21.9331 +/- 2.48361
p2 = 3.36642 +/- 1.25116
****************************************
Chi2 = 1.7669
NDf = 7
Edm = 1.75691e-07
NCalls = 98
p0 = 0.73821 +/- 0.220641 (limited)
p1 = 23.671 +/- 5.18271
p2 = 5.53649 +/- 2.72352
****************************************
MinFCN = 9.70486
Chi2 = 19.4097
NDf = 21
Edm = 8.73736e-08
NCalls = 108
p0 = 1 +/- 0.129925 (limited)
p1 = 30.7473 +/- 2.87702
p2 = 8.76457 +/- 1.97452
****************************************
Chi2 = 2.70826
NDf = 8
Edm = 5.00596e-07
NCalls = 106
p0 = 0.662591 +/- 0.352545 (limited)
p1 = 24.2783 +/- 12.3384
p2 = 7.60846 +/- 6.66009
****************************************
MinFCN = 11.7754
Chi2 = 23.5509
NDf = 22
Edm = 8.43281e-07
NCalls = 108
p0 = 0.865161 +/- 0.102972 (limited)
p1 = 28.7874 +/- 2.92519
p2 = 5.66109 +/- 1.45554
****************************************
Chi2 = 9.74855
NDf = 4
Edm = 3.46464e-07
NCalls = 124
p0 = 0.606488 +/- 0.231103 (limited)
p1 = 22.9147 +/- 5.11615
p2 = 4.88595 +/- 2.18611
****************************************
MinFCN = 14.5599
Chi2 = 29.1197
NDf = 26
Edm = 5.37183e-08
NCalls = 89
p0 = 0.893177 +/- 0.0654554 (limited)
p1 = 26.3026 +/- 1.88872
p2 = 3.66616 +/- 0.981145
****************************************
Chi2 = 3.10119
NDf = 5
Edm = 3.71723e-07
NCalls = 234
p0 = 0.999998 +/- 0.501156 (limited)
p1 = 28.5973 +/- 4.11085
p2 = 8.15931 +/- 3.01069
****************************************
MinFCN = 17.676
Chi2 = 35.352
NDf = 25
Edm = 4.23826e-07
NCalls = 105
p0 = 0.691753 +/- 0.102495 (limited)
p1 = 22.3455 +/- 2.89145
p2 = 5.80589 +/- 1.86419
****************************************
Chi2 = 2.78024
NDf = 7
Edm = 1.5102e-06
NCalls = 82
p0 = 0.65308 +/- 0.206386 (limited)
p1 = 23.0571 +/- 4.95138
p2 = 4.86356 +/- 2.47873
****************************************
MinFCN = 9.65754
Chi2 = 19.3151
NDf = 24
Edm = 2.10929e-06
NCalls = 104
p0 = 1 +/- 0.130796 (limited)
p1 = 31.0119 +/- 2.70979
p2 = 7.55857 +/- 1.6782
****************************************
Chi2 = 3.05436
NDf = 5
Edm = 1.66356e-05
NCalls = 297
p0 = 0.999547 +/- 0.735933 (limited)
p1 = 47.3138 +/- 36.6961
p2 = 43.5419 +/- 61.6394
****************************************
MinFCN = 15.551
Chi2 = 31.1019
NDf = 24
Edm = 3.03617e-07
NCalls = 151
p0 = 1 +/- 0.118805 (limited)
p1 = 32.246 +/- 2.88351
p2 = 8.35109 +/- 1.76088
****************************************
Chi2 = 0.139804
NDf = 2
Edm = 1.06491e-06
NCalls = 91
p0 = 0.660157 +/- 0.258707 (limited)
p1 = 19.2592 +/- 7.6936
p2 = 6.44669 +/- 4.78428
****************************************
MinFCN = 23.3673
Chi2 = 46.7347
NDf = 30
Edm = 1.84329e-06
NCalls = 94
p0 = 0.74715 +/- 0.110543 (limited)
p1 = 28.1656 +/- 7.86858
p2 = 8.19547 +/- 5.07211
****************************************
Chi2 = 2.55321
NDf = 7
Edm = 5.89829e-06
NCalls = 89
p0 = 0.643594 +/- 0.194962 (limited)
p1 = 21.9893 +/- 5.24123
p2 = 5.90243 +/- 2.90213
****************************************
MinFCN = 13.6972
Chi2 = 27.3944
NDf = 22
Edm = 5.81988e-08
NCalls = 86
p0 = 0.788092 +/- 0.0892723 (limited)
p1 = 25.0025 +/- 2.64366
p2 = 4.90379 +/- 1.42976
****************************************
Chi2 = 2.36128
NDf = 6
Edm = 6.99629e-07
NCalls = 88
p0 = 0.560279 +/- 0.13121 (limited)
p1 = 19.8526 +/- 3.03421
p2 = 2.47661 +/- 2.23047
****************************************
MinFCN = 16.199
Chi2 = 32.398
NDf = 22
Edm = 2.10103e-06
NCalls = 62
p0 = 0.693765 +/- 0.0810703 (limited)
p1 = 20.5818 +/- 1.69818
p2 = 3.08945 +/- 0.908341
****************************************
Chi2 = 1.33423
NDf = 7
Edm = 2.89896e-06
NCalls = 102
p0 = 0.564562 +/- 0.203287 (limited)
p1 = 25.8413 +/- 9.79483
p2 = 8.35761 +/- 6.07925
****************************************
MinFCN = 12.5314
Chi2 = 25.0627
NDf = 26
Edm = 1.61089e-07
NCalls = 97
p0 = 0.835727 +/- 0.083548 (limited)
p1 = 30.5594 +/- 4.27567
p2 = 6.90591 +/- 2.2602
****************************************
Chi2 = 1.74047
NDf = 7
Edm = 7.04231e-07
NCalls = 135
p0 = 0.594764 +/- 0.187954 (limited)
p1 = 25.3877 +/- 8.57244
p2 = 6.52667 +/- 4.25157
****************************************
MinFCN = 16.4051
Chi2 = 32.8102
NDf = 26
Edm = 3.55957e-06
NCalls = 78
p0 = 0.710631 +/- 0.082398 (limited)
p1 = 21.9892 +/- 2.24718
p2 = 2.94004 +/- 1.13284
****************************************
Chi2 = 0.310648
NDf = 7
Edm = 2.45348e-06
NCalls = 169
p0 = 0.539725 +/- 0.760718 (limited)
p1 = 12.9065 +/- 72.7676
p2 = 22.8828 +/- 100.306
****************************************
MinFCN = 13.4706
Chi2 = 26.9413
NDf = 25
Edm = 2.38853e-08
NCalls = 153
p0 = 0.812768 +/- 0.131071 (limited)
p1 = 24.5484 +/- 4.86163
p2 = 5.70675 +/- 2.6421
****************************************
Chi2 = 2.52738
NDf = 10
Edm = 1.515e-08
NCalls = 119
p0 = 0.631088 +/- 0.21992 (limited)
p1 = 26.5773 +/- 9.03434
p2 = 8.9826 +/- 4.83446
****************************************
MinFCN = 11.3338
Chi2 = 22.6677
NDf = 23
Edm = 1.90162e-08
NCalls = 71
p0 = 0.745037 +/- 0.103424 (limited)
p1 = 25.6472 +/- 3.41282
p2 = 7.04987 +/- 2.05878
****************************************
Chi2 = 2.51398
NDf = 6
Edm = 6.94471e-07
NCalls = 84
p0 = 0.484246 +/- 0.226988 (limited)
p1 = 18.2432 +/- 5.68591
p2 = 3.93586 +/- 3.23302
****************************************
MinFCN = 10.8867
Chi2 = 21.7734
NDf = 23
Edm = 3.78138e-08
NCalls = 84
p0 = 0.836954 +/- 0.108736 (limited)
p1 = 24.375 +/- 3.34157
p2 = 6.16582 +/- 2.0379
****************************************
Chi2 = 0.946468
NDf = 5
Edm = 5.45857e-06
NCalls = 74
p0 = 0.584615 +/- 0.133896 (limited)
p1 = 19.3728 +/- 3.81107
p2 = 4.20495 +/- 2.53748
****************************************
MinFCN = 12.0156
Chi2 = 24.0312
NDf = 23
Edm = 1.40064e-06
NCalls = 76
p0 = 0.880019 +/- 0.0911312 (limited)
p1 = 28.963 +/- 3.37154
p2 = 6.13976 +/- 1.63654
****************************************
Chi2 = 5.46724
NDf = 8
Edm = 1.55331e-06
NCalls = 99
p0 = 0.763745 +/- 0.233374 (limited)
p1 = 26.3444 +/- 5.03855
p2 = 6.07972 +/- 2.87905
****************************************
MinFCN = 7.09585
Chi2 = 14.1917
NDf = 22
Edm = 2.55685e-07
NCalls = 100
p0 = 1 +/- 0.137512 (limited)
p1 = 31.2245 +/- 2.9769
p2 = 8.50085 +/- 1.97863
****************************************
Chi2 = 0.716283
NDf = 7
Edm = 1.89199e-06
NCalls = 85
p0 = 0.422768 +/- 0.179544 (limited)
p1 = 17.3878 +/- 6.43713
p2 = 3.05887 +/- 4.49587
****************************************
MinFCN = 14.7289
Chi2 = 29.4577
NDf = 25
Edm = 2.3758e-07
NCalls = 81
p0 = 0.74917 +/- 0.103618 (limited)
p1 = 24.7084 +/- 3.46816
p2 = 4.65745 +/- 1.83133
****************************************
Chi2 = 6.40375
NDf = 8
Edm = 5.62321e-07
NCalls = 104
p0 = 0.507615 +/- 0.198193 (limited)
p1 = 22.2924 +/- 5.65071
p2 = 4.8117 +/- 2.67857
****************************************
MinFCN = 14.2056
Chi2 = 28.4112
NDf = 25
Edm = 4.55206e-07
NCalls = 72
p0 = 0.756894 +/- 0.0844728 (limited)
p1 = 22.7347 +/- 2.14529
p2 = 3.73044 +/- 1.05431
****************************************
Chi2 = 3.18171
NDf = 9
Edm = 5.5664e-07
NCalls = 83
p0 = 0.694498 +/- 0.134559 (limited)
p1 = 21.5399 +/- 2.86559
p2 = 3.46906 +/- 1.42287
****************************************
MinFCN = 14.71
Chi2 = 29.4201
NDf = 29
Edm = 1.37273e-09
NCalls = 63
p0 = 0.708238 +/- 0.0850928 (limited)
p1 = 21.4168 +/- 2.75995
p2 = 3.18025 +/- 1.28681
****************************************
Chi2 = 3.13918
NDf = 6
Edm = 4.11187e-06
NCalls = 101
p0 = 0.725096 +/- 0.145408 (limited)
p1 = 25.2372 +/- 3.82188
p2 = 4.88315 +/- 1.80529
****************************************
MinFCN = 9.52542
Chi2 = 19.0508
NDf = 25
Edm = 7.91505e-08
NCalls = 72
p0 = 0.879126 +/- 0.0778689 (limited)
p1 = 29.5534 +/- 2.95061
p2 = 5.14138 +/- 1.41346
****************************************
Chi2 = 3.15774
NDf = 6
Edm = 2.32136e-06
NCalls = 109
p0 = 0.757722 +/- 0.770168 (limited)
p1 = 26.0106 +/- 13.1967
p2 = 7.01687 +/- 5.25991
****************************************
MinFCN = 11.7233
Chi2 = 23.4465
NDf = 21
Edm = 1.90261e-07
NCalls = 89
p0 = 1 +/- 0.073348 (limited)
p1 = 30.5684 +/- 2.60029
p2 = 7.87047 +/- 1.70364
****************************************
Chi2 = 1.90008
NDf = 6
Edm = 9.90083e-06
NCalls = 99
p0 = 0.534999 +/- 0.270262 (limited)
p1 = 24.0906 +/- 7.8809
p2 = 5.63935 +/- 3.24361
****************************************
MinFCN = 16.1477
Chi2 = 32.2953
NDf = 23
Edm = 2.09463e-06
NCalls = 73
p0 = 0.83612 +/- 0.0936713 (limited)
p1 = 25.2247 +/- 3.44688
p2 = 5.16788 +/- 1.95897
****************************************
Chi2 = 2.77855
NDf = 8
Edm = 8.13609e-08
NCalls = 85
p0 = 0.702887 +/- 0.199272 (limited)
p1 = 20.9159 +/- 3.68349
p2 = 4.41504 +/- 2.04434
****************************************
MinFCN = 12.5946
Chi2 = 25.1892
NDf = 22
Edm = 4.03445e-07
NCalls = 53
p0 = 0.686397 +/- 0.100168 (limited)
p1 = 20.697 +/- 2.5238
p2 = 4.27225 +/- 1.40442
****************************************
Chi2 = 4.37217
NDf = 9
Edm = 2.72083e-07
NCalls = 82
p0 = 0.620959 +/- 0.15843 (limited)
p1 = 21.0013 +/- 3.72087
p2 = 4.56895 +/- 2.37229
****************************************
MinFCN = 12.31
Chi2 = 24.62
NDf = 22
Edm = 4.02211e-06
NCalls = 62
p0 = 0.738691 +/- 0.0999045 (limited)
p1 = 21.6956 +/- 2.49688
p2 = 4.68089 +/- 1.47051
****************************************
Chi2 = 1.04047
NDf = 4
Edm = 5.64332e-06
NCalls = 102
p0 = 0.593644 +/- 0.174313 (limited)
p1 = 21.0676 +/- 4.04434
p2 = 3.35047 +/- 2.25854
****************************************
MinFCN = 8.63265
Chi2 = 17.2653
NDf = 25
Edm = 6.38533e-09
NCalls = 101
p0 = 0.893299 +/- 0.0630243 (limited)
p1 = 24.6689 +/- 1.69694
p2 = 2.34492 +/- 0.886976
****************************************
Chi2 = 3.95319
NDf = 10
Edm = 1.32825e-07
NCalls = 96
p0 = 0.574996 +/- 0.152016 (limited)
p1 = 20.2114 +/- 5.1893
p2 = 4.26461 +/- 2.57398
****************************************
MinFCN = 11.4512
Chi2 = 22.9024
NDf = 25
Edm = 9.01028e-07
NCalls = 89
p0 = 0.894533 +/- 0.137242 (limited)
p1 = 31.8196 +/- 6.42723
p2 = 9.36301 +/- 3.43315
****************************************
Chi2 = 1.2121
NDf = 7
Edm = 3.20149e-06
NCalls = 91
p0 = 0.498388 +/- 0.194573 (limited)
p1 = 16.3792 +/- 10.7582
p2 = 4.04759 +/- 14.7395
****************************************
MinFCN = 14.2305
Chi2 = 28.4611
NDf = 27
Edm = 7.65153e-11
NCalls = 112
p0 = 0.568628 +/- 0.0691435 (limited)
p1 = 18.8276 +/- 0.571408
p2 = 0.0507941 +/- 7.32039e-18
****************************************
Chi2 = 1.15843
NDf = 4
Edm = 3.66535e-06
NCalls = 105
p0 = 0.570211 +/- 0.236898 (limited)
p1 = 17.2578 +/- 15.7293
p2 = 9.7494 +/- 16.3952
****************************************
MinFCN = 20.2423
Chi2 = 40.4846
NDf = 29
Edm = 1.41917e-06
NCalls = 139
p0 = 0.612238 +/- 0.0693685 (limited)
p1 = 18.9111 +/- 0.641041
p2 = 0.0810507 +/- 4.47439
****************************************
Chi2 = 4.96865
NDf = 8
Edm = 1.88709e-08
NCalls = 80
p0 = 0.666513 +/- 0.140936 (limited)
p1 = 21.2569 +/- 2.26557
p2 = 3.48413 +/- 2.03653
****************************************
MinFCN = 16.7227
Chi2 = 33.4455
NDf = 22
Edm = 1.37912e-07
NCalls = 60
p0 = 0.671333 +/- 0.0830986 (limited)
p1 = 20.0899 +/- 1.80751
p2 = 3.18801 +/- 0.983175
****************************************
Chi2 = 2.88079
NDf = 4
Edm = 8.70733e-06
NCalls = 96
p0 = 0.803697 +/- 0.275939 (limited)
p1 = 22.1124 +/- 5.26388
p2 = 5.42701 +/- 3.06391
****************************************
MinFCN = 11.2809
Chi2 = 22.5619
NDf = 22
Edm = 1.17703e-06
NCalls = 103
p0 = 1 +/- 0.0550354 (limited)
p1 = 28.1892 +/- 1.93212
p2 = 5.42012 +/- 1.15081
****************************************
Chi2 = 3.96392
NDf = 5
Edm = 7.79729e-08
NCalls = 100
p0 = 0.694889 +/- 0.235894 (limited)
p1 = 23.9686 +/- 5.40538
p2 = 5.07476 +/- 3.36335
****************************************
MinFCN = 10.6942
Chi2 = 21.3884
NDf = 24
Edm = 4.94209e-06
NCalls = 90
p0 = 0.886412 +/- 0.0741325 (limited)
p1 = 26.3919 +/- 2.05984
p2 = 3.75207 +/- 0.962698
****************************************
Chi2 = 0.852791
NDf = 5
Edm = 8.88345e-09
NCalls = 84
p0 = 0.310283 +/- 0.164695 (limited)
p1 = 15.0842 +/- 5.86864
p2 = 2.43104 +/- 3.51103
****************************************
MinFCN = 16.7969
Chi2 = 33.5939
NDf = 22
Edm = 1.06214e-06
NCalls = 90
p0 = 0.858009 +/- 0.0896248 (limited)
p1 = 26.7658 +/- 2.7434
p2 = 5.91245 +/- 1.48212
****************************************
Chi2 = 1.32394
NDf = 6
Edm = 6.16879e-07
NCalls = 86
p0 = 0.672106 +/- 0.201669 (limited)
p1 = 23.2133 +/- 5.10201
p2 = 5.04859 +/- 2.50327
****************************************
MinFCN = 8.61404
Chi2 = 17.2281
NDf = 24
Edm = 6.71438e-08
NCalls = 79
p0 = 0.940369 +/- 0.0595691 (limited)
p1 = 28.7077 +/- 2.62934
p2 = 5.3511 +/- 1.39597
****************************************
Chi2 = 2.48447
NDf = 9
Edm = 3.99523e-06
NCalls = 92
p0 = 0.469573 +/- 0.142912 (limited)
p1 = 18.7922 +/- 3.85884
p2 = 2.98044 +/- 2.31127
****************************************
MinFCN = 10.8641
Chi2 = 21.7281
NDf = 22
Edm = 2.68775e-06
NCalls = 76
p0 = 0.705796 +/- 0.112524 (limited)
p1 = 22.694 +/- 3.20217
p2 = 4.31371 +/- 1.76006
****************************************
Chi2 = 4.05841
NDf = 7
Edm = 3.35768e-06
NCalls = 93
p0 = 0.667164 +/- 0.148637 (limited)
p1 = 21.9757 +/- 2.55643
p2 = 3.34362 +/- 2.015
****************************************
MinFCN = 12.3026
Chi2 = 24.6053
NDf = 24
Edm = 6.94447e-09
NCalls = 70
p0 = 0.771226 +/- 0.0842579 (limited)
p1 = 22.8924 +/- 2.39483
p2 = 4.3482 +/- 1.40708
****************************************
Chi2 = 3.14114
NDf = 6
Edm = 1.74933e-08
NCalls = 114
p0 = 0.532234 +/- 0.174899 (limited)
p1 = 20.0178 +/- 3.71281
p2 = 3.05935 +/- 2.11129
****************************************
MinFCN = 13.6754
Chi2 = 27.3508
NDf = 25
Edm = 3.12686e-06
NCalls = 86
p0 = 0.785653 +/- 0.0837745 (limited)
p1 = 23.5391 +/- 1.85462
p2 = 2.84004 +/- 0.863279
****************************************
Chi2 = 2.88405
NDf = 5
Edm = 1.25252e-05
NCalls = 77
p0 = 0.698497 +/- 0.183511 (limited)
p1 = 21.6581 +/- 4.18422
p2 = 4.04207 +/- 1.56968
****************************************
MinFCN = 16.2927
Chi2 = 32.5855
NDf = 26
Edm = 9.81736e-09
NCalls = 73
p0 = 0.84928 +/- 0.0880232 (limited)
p1 = 26.1083 +/- 2.99956
p2 = 5.04526 +/- 1.47387
****************************************
Chi2 = 0.624725
NDf = 4
Edm = 6.43892e-06
NCalls = 71
p0 = 0.380579 +/- 0.134096 (limited)
p1 = 13.9323 +/- 2.56334
p2 = 1.96554 +/- 1.64705
****************************************
MinFCN = 16.2451
Chi2 = 32.4901
NDf = 24
Edm = 3.46148e-07
NCalls = 111
p0 = 1 +/- 0.13976 (limited)
p1 = 33.5941 +/- 3.2286
p2 = 9.3535 +/- 2.03064
****************************************
Chi2 = 1.67529
NDf = 7
Edm = 4.64318e-08
NCalls = 80
p0 = 0.616278 +/- 0.1576 (limited)
p1 = 18.812 +/- 2.91455
p2 = 3.21096 +/- 1.42859
****************************************
MinFCN = 18.0638
Chi2 = 36.1276
NDf = 26
Edm = 1.22808e-06
NCalls = 66
p0 = 0.675732 +/- 0.0875617 (limited)
p1 = 20.9227 +/- 2.1898
p2 = 3.60151 +/- 1.27833
****************************************
Chi2 = 0.374196
NDf = 2
Edm = 8.80185e-06
NCalls = 80
p0 = 0.685904 +/- 0.174442 (limited)
p1 = 19.998 +/- 1.62445
p2 = 1.71179 +/- 1.75684
****************************************
MinFCN = 17.4763
Chi2 = 34.9527
NDf = 25
Edm = 1.18689e-07
NCalls = 79
p0 = 0.703138 +/- 0.0910538 (limited)
p1 = 20.3182 +/- 1.51335
p2 = 1.05166 +/- 1.00855
****************************************
Chi2 = 2.46931
NDf = 7
Edm = 3.32581e-07
NCalls = 93
p0 = 0.640812 +/- 0.135875 (limited)
p1 = 22.3459 +/- 3.96589
p2 = 4.39764 +/- 2.51185
****************************************
MinFCN = 19.573
Chi2 = 39.1461
NDf = 26
Edm = 1.8708e-07
NCalls = 79
p0 = 0.695688 +/- 0.0960438 (limited)
p1 = 25.9337 +/- 2.91836
p2 = 3.8781 +/- 1.39167
****************************************
Chi2 = 2.49631
NDf = 3
Edm = 6.6234e-06
NCalls = 102
p0 = 0.611704 +/- 0.35871 (limited)
p1 = 20.7057 +/- 8.42105
p2 = 5.08053 +/- 3.9281
****************************************
MinFCN = 19.5603
Chi2 = 39.1206
NDf = 22
Edm = 2.27081e-08
NCalls = 74
p0 = 0.700633 +/- 0.0849755 (limited)
p1 = 19.1288 +/- 1.84326
p2 = 3.20784 +/- 1.0308
****************************************
Chi2 = 0.418946
NDf = 2
Edm = 7.44661e-07
NCalls = 53
p0 = 0.60361 +/- 0.106733 (limited)
p1 = 15.7806 +/- 2
p2 = 0.105266 +/- 2
****************************************
MinFCN = 19.3993
Chi2 = 38.7986
NDf = 23
Edm = 9.2223e-06
NCalls = 245
p0 = 0.644389 +/- 0.0711313 (limited)
p1 = 18.1356 +/- 0.714145
p2 = 0.0157025 +/- 0.682189
****************************************
Chi2 = 3.54456
NDf = 5
Edm = 2.33566e-06
NCalls = 85
p0 = 0.527397 +/- 0.217626 (limited)
p1 = 17.9928 +/- 6.38912
p2 = 5.4498 +/- 3.84602
****************************************
MinFCN = 12.2163
Chi2 = 24.4327
NDf = 20
Edm = 6.3676e-06
NCalls = 80
p0 = 0.859519 +/- 0.0906147 (limited)
p1 = 25.943 +/- 3.43909
p2 = 6.71027 +/- 2.02884
****************************************
Chi2 = 3.23312
NDf = 8
Edm = 9.46056e-07
NCalls = 70
p0 = 0.515942 +/- 0.0980029 (limited)
p1 = 17.2963 +/- 1.44299
p2 = 1.9009 +/- 1.23849
****************************************
MinFCN = 11.3898
Chi2 = 22.7795
NDf = 20
Edm = 6.32872e-09
NCalls = 72
p0 = 0.633638 +/- 0.0838664 (limited)
p1 = 18.524 +/- 1.68856
p2 = 2.16871 +/- 1.02224
****************************************
Chi2 = 5.28211
NDf = 11
Edm = 1.87776e-06
NCalls = 71
p0 = 0.612568 +/- 0.109907 (limited)
p1 = 19.3198 +/- 2.18618
p2 = 3.37801 +/- 1.31028
****************************************
MinFCN = 9.91351
Chi2 = 19.827
NDf = 22
Edm = 2.00204e-07
NCalls = 62
p0 = 0.636118 +/- 0.097181 (limited)
p1 = 19.5971 +/- 2.68815
p2 = 3.88968 +/- 1.7373
****************************************
Chi2 = 2.51155
NDf = 7
Edm = 2.60724e-06
NCalls = 74
p0 = 0.647126 +/- 0.147452 (limited)
p1 = 20.8474 +/- 2.85119
p2 = 3.27715 +/- 1.66359
****************************************
MinFCN = 6.94327
Chi2 = 13.8865
NDf = 22
Edm = 4.86511e-06
NCalls = 73
p0 = 0.901211 +/- 0.0749805 (limited)
p1 = 24.7879 +/- 2.21116
p2 = 3.76426 +/- 1.07742
****************************************
Chi2 = 2.33728
NDf = 6
Edm = 7.37813e-07
NCalls = 109
p0 = 0.624689 +/- 0.141987 (limited)
p1 = 19.3681 +/- 3.57572
p2 = 3.40927 +/- 2.17685
****************************************
MinFCN = 14.2977
Chi2 = 28.5955
NDf = 24
Edm = 3.94252e-10
NCalls = 81
p0 = 0.832764 +/- 0.0867739 (limited)
p1 = 24.0485 +/- 2.82721
p2 = 4.07159 +/- 1.4461
****************************************
Chi2 = 3.75642
NDf = 8
Edm = 5.68096e-06
NCalls = 120
p0 = 0.387014 +/- 0.0702296 (limited)
p1 = 11.5811 +/- 8.22684
p2 = 0.313997 +/- 4.44032
****************************************
MinFCN = 18.3537
Chi2 = 36.7074
NDf = 24
Edm = 3.14223e-08
NCalls = 122
p0 = 0.766056 +/- 0.130733 (limited)
p1 = 26.3265 +/- 5.29894
p2 = 8.25159 +/- 3.37803
****************************************
Chi2 = 1.68054
NDf = 6
Edm = 5.00607e-06
NCalls = 79
p0 = 0.492763 +/- 0.200749 (limited)
p1 = 18.8758 +/- 5.209
p2 = 3.88829 +/- 2.85902
****************************************
MinFCN = 12.5237
Chi2 = 25.0474
NDf = 21
Edm = 6.19402e-09
NCalls = 83
p0 = 0.82576 +/- 0.0905004 (limited)
p1 = 24.7459 +/- 2.64975
p2 = 5.53589 +/- 1.50229
****************************************
Chi2 = 1.37515
NDf = 4
Edm = 3.40318e-06
NCalls = 106
p0 = 0.759679 +/- 0.234791 (limited)
p1 = 24.2145 +/- 5.44887
p2 = 4.93415 +/- 2.65778
****************************************
MinFCN = 9.98776
Chi2 = 19.9755
NDf = 23
Edm = 6.74125e-07
NCalls = 88
p0 = 0.922627 +/- 0.053996 (limited)
p1 = 25.2002 +/- 1.76064
p2 = 3.37452 +/- 0.879146
****************************************
Chi2 = 2.35692
NDf = 4
Edm = 1.08773e-07
NCalls = 81
p0 = 0.373315 +/- 0.215845 (limited)
p1 = 12.4572 +/- 7.57085
p2 = 4.00427 +/- 8.97995
****************************************
MinFCN = 15.2686
Chi2 = 30.5373
NDf = 24
Edm = 4.23993e-08
NCalls = 154
p0 = 1 +/- 0.165147 (limited)
p1 = 30.0737 +/- 2.81991
p2 = 7.24184 +/- 1.65777
****************************************
Chi2 = 1.93137
NDf = 7
Edm = 4.79943e-09
NCalls = 113
p0 = 0.632872 +/- 0.231351 (limited)
p1 = 27.1811 +/- 8.5188
p2 = 6.83092 +/- 3.30519
****************************************
MinFCN = 11.4871
Chi2 = 22.9743
NDf = 24
Edm = 3.13018e-07
NCalls = 73
p0 = 0.886287 +/- 0.0822954 (limited)
p1 = 26.4994 +/- 2.79725
p2 = 5.06979 +/- 1.36513
****************************************
Chi2 = 3.28016
NDf = 6
Edm = 6.04893e-06
NCalls = 99
p0 = 0.696957 +/- 0.193092 (limited)
p1 = 22.9427 +/- 3.44124
p2 = 3.63739 +/- 2.36972
****************************************
MinFCN = 14.002
Chi2 = 28.0041
NDf = 25
Edm = 3.57658e-07
NCalls = 62
p0 = 0.820512 +/- 0.0837157 (limited)
p1 = 24.7539 +/- 2.2824
p2 = 4.0766 +/- 1.13837
****************************************
Chi2 = 2.56902
NDf = 7
Edm = 5.20615e-07
NCalls = 94
p0 = 0.68832 +/- 0.19603 (limited)
p1 = 24.2988 +/- 4.41739
p2 = 4.93562 +/- 3.1133
****************************************
MinFCN = 10.1565
Chi2 = 20.313
NDf = 23
Edm = 4.51533e-06
NCalls = 73
p0 = 0.83692 +/- 0.100458 (limited)
p1 = 26.5351 +/- 2.71955
p2 = 4.32699 +/- 1.33756
****************************************
Chi2 = 3.04459
NDf = 7
Edm = 7.4353e-07
NCalls = 83
p0 = 0.659997 +/- 0.249426 (limited)
p1 = 22.9747 +/- 5.95617
p2 = 5.36022 +/- 2.66473
****************************************
MinFCN = 11.1635
Chi2 = 22.327
NDf = 21
Edm = 1.52311e-08
NCalls = 72
p0 = 0.797119 +/- 0.109369 (limited)
p1 = 23.7528 +/- 3.02536
p2 = 5.51075 +/- 1.78264
****************************************
Chi2 = 6.27397
NDf = 8
Edm = 5.29961e-07
NCalls = 81
p0 = 0.662433 +/- 0.15714 (limited)
p1 = 21.5909 +/- 3.29623
p2 = 4.09179 +/- 1.74745
****************************************
MinFCN = 14.006
Chi2 = 28.012
NDf = 23
Edm = 1.73409e-07
NCalls = 73
p0 = 0.74949 +/- 0.087125 (limited)
p1 = 22.4394 +/- 2.25986
p2 = 3.18063 +/- 1.06939
****************************************
Chi2 = 1.94311
NDf = 9
Edm = 1.89133e-07
NCalls = 106
p0 = 0.575157 +/- 0.298322 (limited)
p1 = 25.6868 +/- 11.7079
p2 = 7.54114 +/- 5.74853
****************************************
MinFCN = 7.95143
Chi2 = 15.9029
NDf = 22
Edm = 3.34787e-06
NCalls = 100
p0 = 1 +/- 0.0861316 (limited)
p1 = 33.4794 +/- 3.24851
p2 = 9.96621 +/- 2.27222
****************************************
Chi2 = 2.75509
NDf = 9
Edm = 9.98946e-08
NCalls = 69
p0 = 0.593401 +/- 0.101469 (limited)
p1 = 18.8032 +/- 2.57519
p2 = 2.53183 +/- 1.7654
****************************************
MinFCN = 8.82691
Chi2 = 17.6538
NDf = 19
Edm = 8.94292e-07
NCalls = 66
p0 = 0.707869 +/- 0.0806949 (limited)
p1 = 20.75 +/- 1.52055
p2 = 2.05399 +/- 0.709689
****************************************
Chi2 = 2.54952
NDf = 6
Edm = 4.57669e-08
NCalls = 96
p0 = 0.660242 +/- 0.259374 (limited)
p1 = 25.0771 +/- 5.98352
p2 = 5.39543 +/- 2.98249
****************************************
MinFCN = 13.093
Chi2 = 26.1861
NDf = 25
Edm = 7.24454e-07
NCalls = 63
p0 = 0.822936 +/- 0.0852676 (limited)
p1 = 26.505 +/- 2.8571
p2 = 4.82335 +/- 1.47173
****************************************
Chi2 = 4.62283
NDf = 10
Edm = 1.36401e-08
NCalls = 89
p0 = 0.592713 +/- 0.183874 (limited)
p1 = 20.9349 +/- 5.53213
p2 = 6.39618 +/- 4.21336
****************************************
MinFCN = 10.8024
Chi2 = 21.6048
NDf = 22
Edm = 3.61653e-08
NCalls = 73
p0 = 0.718975 +/- 0.133739 (limited)
p1 = 24.3254 +/- 4.59911
p2 = 7.31889 +/- 3.07985
****************************************
Chi2 = 5.3127
NDf = 6
Edm = 2.53153e-06
NCalls = 119
p0 = 0.534666 +/- 0.0847463 (limited)
p1 = 12.0856 +/- 13.9766
p2 = 0.685012 +/- 8.82276
****************************************
MinFCN = 16.3818
Chi2 = 32.7636
NDf = 22
Edm = 3.8063e-06
NCalls = 100
p0 = 0.789732 +/- 0.103694 (limited)
p1 = 24.4115 +/- 2.95524
p2 = 4.45708 +/- 1.48761
****************************************
Chi2 = 0.968364
NDf = 7
Edm = 1.15106e-06
NCalls = 74
p0 = 0.669971 +/- 0.134042 (limited)
p1 = 19.9248 +/- 3.66311
p2 = 4.7186 +/- 3.31403
****************************************
MinFCN = 15.3613
Chi2 = 30.7226
NDf = 24
Edm = 5.15702e-06
NCalls = 88
p0 = 0.780567 +/- 0.0894369 (limited)
p1 = 25.9084 +/- 2.75967
p2 = 4.59539 +/- 1.41025
****************************************
Chi2 = 2.88345
NDf = 10
Edm = 2.24225e-06
NCalls = 102
p0 = 0.629842 +/- 0.174064 (limited)
p1 = 21.9766 +/- 6.0423
p2 = 6.83408 +/- 3.9968
****************************************
MinFCN = 9.27297
Chi2 = 18.5459
NDf = 20
Edm = 1.87394e-06
NCalls = 74
p0 = 0.89538 +/- 0.174255 (limited)
p1 = 32.6871 +/- 8.87808
p2 = 12.1149 +/- 5.18796
****************************************
Chi2 = 1.80215
NDf = 6
Edm = 2.68316e-07
NCalls = 87
p0 = 0.495591 +/- 0.211145 (limited)
p1 = 19.645 +/- 5.2052
p2 = 3.59211 +/- 2.51889
****************************************
MinFCN = 11.3263
Chi2 = 22.6526
NDf = 23
Edm = 6.21131e-07
NCalls = 85
p0 = 0.921303 +/- 0.0720411 (limited)
p1 = 26.5793 +/- 2.38289
p2 = 5.11338 +/- 1.20119
****************************************
Chi2 = 3.79465
NDf = 6
Edm = 4.35871e-08
NCalls = 69
p0 = 0.611171 +/- 0.128277 (limited)
p1 = 17.467 +/- 2.93532
p2 = 3.02848 +/- 1.64432
****************************************
MinFCN = 16.2411
Chi2 = 32.4822
NDf = 24
Edm = 5.63919e-07
NCalls = 84
p0 = 0.887021 +/- 0.149113 (limited)
p1 = 28.9301 +/- 6.59512
p2 = 7.99154 +/- 3.69369
****************************************
Chi2 = 2.748
NDf = 7
Edm = 5.78153e-09
NCalls = 140
p0 = 1 +/- 0.733966 (limited)
p1 = 28.7334 +/- 2.38732
p2 = 6.33261 +/- 1.85434
****************************************
MinFCN = 14.7257
Chi2 = 29.4515
NDf = 25
Edm = 6.17545e-08
NCalls = 98
p0 = 0.793408 +/- 0.149393 (limited)
p1 = 25.3941 +/- 5.1633
p2 = 6.20929 +/- 3.20508
****************************************
Chi2 = 4.29305
NDf = 9
Edm = 3.06585e-06
NCalls = 82
p0 = 0.687721 +/- 0.16847 (limited)
p1 = 22.2779 +/- 3.60769
p2 = 4.13806 +/- 1.75728
****************************************
MinFCN = 6.51615
Chi2 = 13.0323
NDf = 21
Edm = 2.56493e-06
NCalls = 80
p0 = 0.929011 +/- 0.128044 (limited)
p1 = 26.8551 +/- 4.60022
p2 = 6.16639 +/- 2.6095
****************************************
Chi2 = 1.74986
NDf = 2
Edm = 2.69957e-06
NCalls = 256
p0 = 0.999951 +/- 0.988093 (limited)
p1 = 33.6961 +/- 9.16268
p2 = 13.7955 +/- 8.24703
****************************************
MinFCN = 21.3855
Chi2 = 42.7711
NDf = 26
Edm = 4.23082e-07
NCalls = 149
p0 = 0.808068 +/- 0.0853178 (limited)
p1 = 26.8921 +/- 2.88537
p2 = 6.0004 +/- 1.56206
****************************************
Chi2 = 4.72905
NDf = 5
Edm = 2.89445e-07
NCalls = 67
p0 = 0.417412 +/- 0.107227 (limited)
p1 = 14.5796 +/- 2.95636
p2 = 2.22066 +/- 2.12966
****************************************
MinFCN = 20.7746
Chi2 = 41.5492
NDf = 25
Edm = 4.86099e-06
NCalls = 86
p0 = 0.780136 +/- 0.0893488 (limited)
p1 = 24.5549 +/- 2.10448
p2 = 4.36318 +/- 1.12085
****************************************
Chi2 = 2.45643
NDf = 6
Edm = 2.63752e-06
NCalls = 99
p0 = 0.554001 +/- 0.226655 (limited)
p1 = 23.9121 +/- 6.69531
p2 = 6.04267 +/- 3.44117
****************************************
MinFCN = 13.3134
Chi2 = 26.6268
NDf = 25
Edm = 5.83165e-09
NCalls = 81
p0 = 0.859757 +/- 0.0748063 (limited)
p1 = 25.7851 +/- 2.03938
p2 = 4.58085 +/- 1.11229
****************************************
Chi2 = 2.91637
NDf = 4
Edm = 1.377e-05
NCalls = 84
p0 = 0.769946 +/- 0.185015 (limited)
p1 = 20.5779 +/- 2.52006
p2 = 3.50084 +/- 1.35396
****************************************
MinFCN = 18.6117
Chi2 = 37.2235
NDf = 24
Edm = 1.80945e-07
NCalls = 72
p0 = 0.788394 +/- 0.104211 (limited)
p1 = 24.2646 +/- 3.57577
p2 = 5.17213 +/- 2.03607
****************************************
Chi2 = 1.21412
NDf = 6
Edm = 1.16053e-08
NCalls = 141
p0 = 0.632519 +/- 0.106789 (limited)
p1 = 17.4834 +/- 1.66297
p2 = 1.44082 +/- 1.10945
****************************************
MinFCN = 16.0874
Chi2 = 32.1748
NDf = 25
Edm = 1.23857e-08
NCalls = 73
p0 = 0.683032 +/- 0.0852759 (limited)
p1 = 20.5028 +/- 2.71991
p2 = 2.79578 +/- 1.30889
#include <TVirtualFitter.h>
#include <TH1.h>
#include <TRandom3.h>
#include <TF1.h>
#include <TFitResult.h>
#include <TStyle.h>
#include <TCanvas.h>
#include <TLegend.h>
#include <TPaveStats.h>
#include <TGraphErrors.h>
#include <TObjArray.h>
#include <HFitInterface.h>
#include <Fit/BinData.h>
#include <cassert>
#include <iostream>
void TestBinomial(int nloop = 100, int nevts = 100, bool plot = false, bool debug = false, int seed = 111)
{
TObjArray hbiasNorm;
TObjArray hbiasThreshold;
TObjArray hbiasWidth;
TH1D* hChisquared = new TH1D("hChisquared",
"#chi^{2} probability (Baker-Cousins)", 200, 0.0, 1.0);
// Note: in order to be able to use TH1::FillRandom() to generate
// pseudo-experiments, we use a trick: generate "selected"
// and "non-selected" samples independently. These are
// statistically independent and therefore can be safely
// added to yield the "before selection" sample.
// Define (arbitrarily?) a distribution of input events.
// Here: assume a x^(-2) distribution. Boundaries: [10, 100].
double xmin =10, xmax = 100;
TH1D* hM2D = new TH1D("hM2D", "x^(-2) denominator distribution",
45, xmin, xmax);
TH1D* hM2N = new TH1D("hM2N", "x^(-2) numerator distribution",
45, xmin, xmax);
TH1D* hM2E = new TH1D("hM2E", "x^(-2) efficiency",
45, xmin, xmax);
TF1* fM2D = new TF1("fM2D", "(1-[0]/(1+exp(([1]-x)/[2])))/(x*x)",
TF1* fM2N = new TF1("fM2N", "[0]/(1+exp(([1]-x)/[2]))/(x*x)",
TF1* fM2Fit = new TF1("fM2Fit", "[0]/(1+exp(([1]-x)/[2]))",
TF1* fM2Fit2 = nullptr;
TRandom3 rb(seed);
// First try: use a single set of parameters.
// For each try, we need to find the overall normalization
double normalization = 0.80;
double threshold = 25.0;
double width = 5.0;
fM2D->SetParameter(0, normalization);
fM2D->SetParameter(1, threshold);
fM2D->SetParameter(2, width);
fM2N->SetParameter(0, normalization);
fM2N->SetParameter(1, threshold);
fM2N->SetParameter(2, width);
double integralN = fM2N->Integral(xmin, xmax);
double integralD = fM2D->Integral(xmin, xmax);
double fracN = integralN/(integralN+integralD);
int nevtsN = rb.Binomial(nevts, fracN);
int nevtsD = nevts - nevtsN;
std::cout << nevtsN << " " << nevtsD << std::endl;
gStyle->SetOptFit(1111);
// generate many times to see the bias
for (int iloop = 0; iloop < nloop; ++iloop) {
// generate pseudo-experiments
hM2D->Reset();
hM2N->Reset();
hM2D->FillRandom(fM2D->GetName(), nevtsD);
hM2N->FillRandom(fM2N->GetName(), nevtsN);
// construct the "efficiency" histogram
hM2N->Sumw2();
hM2E->Divide(hM2N, hM2D, 1, 1, "b");
// Fit twice, using the same fit function.
// In the first (standard) fit, initialize to (arbitrary) values.
// In the second fit, use the results from the first fit (this
// makes it easier for the fit -- but the purpose here is not to
// show how easy or difficult it is to obtain results, but whether
// the CORRECT results are obtained or not!).
fM2Fit->SetParameter(0, 0.5);
fM2Fit->SetParameter(1, 15.0);
fM2Fit->SetParameter(2, 2.0);
fM2Fit->SetParError(0, 0.1);
fM2Fit->SetParError(1, 1.0);
fM2Fit->SetParError(2, 0.2);
TH1 * hf = fM2Fit->GetHistogram();
// std::cout << "Function values " << std::endl;
// for (int i = 1; i <= hf->GetNbinsX(); ++i)
// std::cout << hf->GetBinContent(i) << " ";
// std::cout << std::endl;
TCanvas* cEvt;
if (plot) {
cEvt = new TCanvas(Form("cEnv%d",iloop),
Form("plots for experiment %d", iloop),
1000, 600);
cEvt->Divide(1,2);
cEvt->cd(1);
hM2D->DrawCopy("HIST");
hM2N->DrawCopy("HIST SAME");
cEvt->cd(2);
}
for (int fit = 0; fit < 2; ++fit) {
int status = 0;
switch (fit) {
case 0:
{
// new TCanvas();
// fM2Fit->Draw();
TString optFit = "RN";
if (debug) optFit += TString("SV");
TFitResultPtr res = hM2E->Fit(fM2Fit, optFit);
if (plot) {
hM2E->DrawCopy("E");
fM2Fit->SetLineColor(kBlue);
fM2Fit->DrawCopy("SAME");
}
if (debug) res->Print();
status = res;
break;
}
case 1:
{
// if (fM2Fit2) delete fM2Fit2;
// fM2Fit2 = dynamic_cast<TF1*>(fM2Fit->Clone("fM2Fit2"));
fM2Fit2 = fM2Fit; // do not clone/copy the function
if (fM2Fit2->GetParameter(0) >= 1.0)
fM2Fit2->SetParameter(0, 0.95);
fM2Fit2->SetParLimits(0, 0.0, 1.0);
// new TCanvas();
// fM2Fit2->Draw();
TBinomialEfficiencyFitter bef(hM2N, hM2D);
TString optFit = "RI S";
if (debug) optFit += TString("V");
TFitResultPtr res = bef.Fit(fM2Fit2,optFit);
status = res;
if (status !=0) {
std::cerr << "Error performing binomial efficiency fit, result = "
<< status << std::endl;
res->Print();
continue;
}
if (plot) {
fM2Fit2->SetLineColor(kRed);
fM2Fit2->DrawCopy("SAME");
bool confint = (status == 0);
if (confint) {
// compute confidence interval on fitted function
auto htemp = fM2Fit2->GetHistogram();
ROOT::Fit::FillData(xdata, fM2Fit2->GetHistogram() );
res->GetConfidenceIntervals(xdata, gr.GetEY(), 0.68, false);
gr.DrawClone("4 same");
}
}
if (debug) {
res->Print();
}
}
}
if (status != 0) break;
double fnorm = fM2Fit->GetParameter(0);
double enorm = fM2Fit->GetParError(0);
double fthreshold = fM2Fit->GetParameter(1);
double ethreshold = fM2Fit->GetParError(1);
double fwidth = fM2Fit->GetParameter(2);
double ewidth = fM2Fit->GetParError(2);
if (fit == 1) {
fnorm = fM2Fit2->GetParameter(0);
enorm = fM2Fit2->GetParError(0);
fthreshold = fM2Fit2->GetParameter(1);
ethreshold = fM2Fit2->GetParError(1);
fwidth = fM2Fit2->GetParameter(2);
ewidth = fM2Fit2->GetParError(2);
hChisquared->Fill(fM2Fit2->GetProb());
}
TH1D* h = dynamic_cast<TH1D*>(hbiasNorm[fit]);
h->Fill((fnorm-normalization)/enorm);
h = dynamic_cast<TH1D*>(hbiasThreshold[fit]);
h->Fill((fthreshold-threshold)/ethreshold);
h = dynamic_cast<TH1D*>(hbiasWidth[fit]);
h->Fill((fwidth-width)/ewidth);
}
}
TCanvas* c1 = new TCanvas("c1",
"Efficiency fit biases",10,10,1000,800);
c1->Divide(2,2);
TH1D *h0, *h1;
c1->cd(1);
h0 = dynamic_cast<TH1D*>(hbiasNorm[0]);
h0->Draw("HIST");
h1 = dynamic_cast<TH1D*>(hbiasNorm[1]);
h1->Draw("HIST SAMES");
TLegend* l1 = new TLegend(0.1, 0.75, 0.5, 0.9,
"plateau parameter", "ndc");
l1->AddEntry(h0, Form("histogram: mean = %4.2f RMS = \
%4.2f", h0->GetMean(), h0->GetRMS()), "l");
l1->AddEntry(h1, Form("binomial : mean = %4.2f RMS = \
%4.2f", h1->GetMean(), h1->GetRMS()), "l");
l1->Draw();
c1->cd(2);
h0 = dynamic_cast<TH1D*>(hbiasThreshold[0]);
h0->Draw("HIST");
h1 = dynamic_cast<TH1D*>(hbiasThreshold[1]);
h1->Draw("HIST SAMES");
TLegend* l2 = new TLegend(0.1, 0.75, 0.5, 0.9,
"threshold parameter", "ndc");
l2->AddEntry(h0, Form("histogram: mean = %4.2f RMS = \
%4.2f", h0->GetMean(), h0->GetRMS()), "l");
l2->AddEntry(h1, Form("binomial : mean = %4.2f RMS = \
%4.2f", h1->GetMean(), h1->GetRMS()), "l");
l2->Draw();
c1->cd(3);
h0 = dynamic_cast<TH1D*>(hbiasWidth[0]);
h0->Draw("HIST");
h1 = dynamic_cast<TH1D*>(hbiasWidth[1]);
h1->Draw("HIST SAMES");
TLegend* l3 = new TLegend(0.1, 0.75, 0.5, 0.9, "width parameter", "ndc");
l3->AddEntry(h0, Form("histogram: mean = %4.2f RMS = \
%4.2f", h0->GetMean(), h0->GetRMS()), "l");
l3->AddEntry(h1, Form("binomial : mean = %4.2f RMS = \
%4.2f", h1->GetMean(), h1->GetRMS()), "l");
l3->Draw();
c1->cd(4);
hChisquared->Draw("HIST");
}
int main() {
TestBinomial();
}
int main()
Definition Prototype.cxx:12
#define h(i)
Definition RSha256.hxx:106
@ kRed
Definition Rtypes.h:66
@ kBlue
Definition Rtypes.h:66
winID h TVirtualViewer3D TVirtualGLPainter char TVirtualGLPainter plot
Option_t Option_t width
float xmin
float xmax
char * Form(const char *fmt,...)
Formats a string in a circular formatting buffer.
Definition TString.cxx:2489
R__EXTERN TStyle * gStyle
Definition TStyle.h:433
Class describing the binned data sets : vectors of x coordinates, y values and optionally error on y ...
Definition BinData.h:52
void GetConfidenceIntervals(unsigned int n, unsigned int stride1, unsigned int stride2, const double *x, double *ci, double cl=0.95, bool norm=false) const
get confidence intervals for an array of n points x.
static void SetDefaultIntegrator(const char *name)
virtual void SetFillColor(Color_t fcolor)
Set the fill area color.
Definition TAttFill.h:37
virtual void SetFillStyle(Style_t fstyle)
Set the fill area style.
Definition TAttFill.h:39
virtual void SetLineWidth(Width_t lwidth)
Set the line width.
Definition TAttLine.h:43
virtual void SetLineColor(Color_t lcolor)
Set the line color.
Definition TAttLine.h:40
virtual void SetMarkerStyle(Style_t mstyle=1)
Set the marker style.
Definition TAttMarker.h:40
Binomial fitter for the division of two histograms.
The Canvas class.
Definition TCanvas.h:23
Definition TCanvas.cxx:716
1-Dim function class
Definition TF1.h:233
virtual void SetParError(Int_t ipar, Double_t error)
Set error for parameter number ipar.
Definition TF1.cxx:3479
virtual TH1 * GetHistogram() const
Return a pointer to the histogram used to visualise the function Note that this histogram is managed ...
Definition TF1.cxx:1586
virtual Double_t GetParError(Int_t ipar) const
Return value of parameter number ipar.
Definition TF1.cxx:1932
virtual Double_t GetProb() const
Return the fit probability.
Definition TF1.cxx:1957
virtual Double_t Integral(Double_t a, Double_t b, Double_t epsrel=1.e-12)
IntegralOneDim or analytical integral.
Definition TF1.cxx:2531
virtual void SetParLimits(Int_t ipar, Double_t parmin, Double_t parmax)
Set lower and upper limits for parameter ipar.
Definition TF1.cxx:3507
virtual TF1 * DrawCopy(Option_t *option="") const
Draw a copy of this function with its current attributes.
Definition TF1.cxx:1365
virtual void SetParameter(Int_t param, Double_t value)
Definition TF1.h:660
virtual Double_t GetParameter(Int_t ipar) const
Definition TF1.h:538
Provides an indirection to the TFitResult class and with a semantics identical to a TFitResult pointe...
void Print(Option_t *option="") const override
Print result of the fit, by default chi2, parameter values and errors.
A TGraphErrors is a TGraph with error bars.
Double_t * GetEY() const override
1-D histogram with a double per channel (see TH1 documentation)
Definition TH1.h:669
void Reset(Option_t *option="") override
Reset.
Definition TH1.cxx:10459
TH1 is the base class of all histogram classes in ROOT.
Definition TH1.h:59
virtual Double_t GetMean(Int_t axis=1) const
For axis = 1,2 or 3 returns the mean value of the histogram along X,Y or Z axis.
Definition TH1.cxx:7503
virtual void FillRandom(const char *fname, Int_t ntimes=5000, TRandom *rng=nullptr)
Fill histogram following distribution in function fname.
Definition TH1.cxx:3519
virtual TFitResultPtr Fit(const char *formula, Option_t *option="", Option_t *goption="", Double_t xmin=0, Double_t xmax=0)
Fit histogram with function fname.
Definition TH1.cxx:3898
virtual Bool_t Add(TF1 *h1, Double_t c1=1, Option_t *option="")
Performs the operation: this = this + c1*f1 if errors are defined (see TH1::Sumw2),...
Definition TH1.cxx:826
virtual Int_t Fill(Double_t x)
Increment bin with abscissa X by 1.
Definition TH1.cxx:3344
void Draw(Option_t *option="") override
Draw this histogram with options.
Definition TH1.cxx:3066
Double_t GetRMS(Int_t axis=1) const
This function returns the Standard Deviation (Sigma) of the distribution not the Root Mean Square (RM...
Definition TH1.h:319
virtual TH1 * DrawCopy(Option_t *option="", const char *name_postfix="_copy") const
Copy this histogram and Draw in the current pad.
Definition TH1.cxx:3113
virtual Bool_t Divide(TF1 *f1, Double_t c1=1)
Performs the operation: this = this/(c1*f1) if errors are defined (see TH1::Sumw2),...
Definition TH1.cxx:2840
virtual void Sumw2(Bool_t flag=kTRUE)
Create structure to store sum of squares of weights.
Definition TH1.cxx:8988
This class displays a legend box (TPaveText) containing several legend entries.
Definition TLegend.h:23
TLegendEntry * AddEntry(const TObject *obj, const char *label="", Option_t *option="lpf")
Add a new entry to this legend.
Definition TLegend.cxx:317
void Draw(Option_t *option="") override
Draw this legend with its current attributes.
Definition TLegend.cxx:422
const char * GetName() const override
Returns name of object.
Definition TNamed.h:47
An array of TObjects.
Definition TObjArray.h:31
Definition TObjArray.h:68
virtual TObject * DrawClone(Option_t *option="") const
Draw a clone of this object in the current selected pad with: gROOT->SetSelectedPad(c1).
Definition TObject.cxx:299
void Divide(Int_t nx=1, Int_t ny=1, Float_t xmargin=0.01, Float_t ymargin=0.01, Int_t color=0) override
Random number generator class based on M.
Definition TRandom3.h:27
Basic string class.
Definition TString.h:139
void SetOptStat(Int_t stat=1)
The type of information printed in the histogram statistics box can be selected via the parameter mod...
Definition TStyle.cxx:1636
void SetOptFit(Int_t fit=1)
The type of information about fit parameters printed in the histogram statistics box can be selected ...
Definition TStyle.cxx:1589
static void SetDefaultFitter(const char *name="")
static: set name of default fitter
return c1
Definition legend1.C:41
TGraphErrors * gr
Definition legend1.C:25
TH1F * h1
Definition legend1.C:5