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Re: (meteorobs) Population index error
> I calculated some population indexes, but I don't know
> how to calculate error...
> Is it standard error, or something else?
> Nikola
The error of the population index can only be derived by
numerical simulations. this works like this: you generate
random magnitude distributions following a distribution
as given by your population index, but containing a certain
number of meteors (the number you had for the pop index).
then you compute the pop index from this distr. it will be
different from your input-r, because the distributions has
a natural noise. you do this many many times. Then you see
that the pop indices you get (all with the same input-r)
have a certain scatter around your input-r. This scatter is
the error of the pop index you derived from the real meteors
(which is the same as the input-r for the random distributions).
The pop index is thus a function of the number of meteors
and the pop index itself.
Here is a prepared file derived from simulations:
r N error
---------------
1.1 10 0.0758
1.1 15 0.0580
1.1 22 0.0457
1.1 33 0.0378
1.1 49 0.0302
1.1 73 0.0239
1.1 109 0.0196
1.1 163 0.0167
1.1 244 0.0136
1.1 366 0.0114
1.1 549 0.0095
1.1 823 0.0085
1.1 1234 0.0073
1.1 1851 0.0063
1.1 2776 0.0057
1.1 4164 0.0054
1.1 6246 0.0050
1.1 9369 0.0050
1.2 10 0.1323
1.2 15 0.0993
1.2 22 0.0813
1.2 33 0.0643
1.2 49 0.0521
1.2 73 0.0427
1.2 109 0.0356
1.2 163 0.0289
1.2 244 0.0237
1.2 366 0.0195
1.2 549 0.0157
1.2 823 0.0129
1.2 1234 0.0108
1.2 1851 0.0089
1.2 2776 0.0074
1.2 4164 0.0063
1.2 6246 0.0055
1.2 9369 0.0051
1.3 10 0.1860
1.3 15 0.1358
1.3 22 0.1016
1.3 33 0.0814
1.3 49 0.0672
1.3 73 0.0550
1.3 109 0.0426
1.3 163 0.0361
1.3 244 0.0287
1.3 366 0.0239
1.3 549 0.0194
1.3 823 0.0156
1.3 1234 0.0132
1.3 1851 0.0109
1.3 2776 0.0090
1.3 4164 0.0075
1.3 6246 0.0063
1.3 9369 0.0055
1.4 10 0.2409
1.4 15 0.1674
1.4 22 0.1275
1.4 33 0.1003
1.4 49 0.0785
1.4 73 0.0668
1.4 109 0.0536
1.4 163 0.0432
1.4 244 0.0355
1.4 366 0.0289
1.4 549 0.0236
1.4 823 0.0192
1.4 1234 0.0160
1.4 1851 0.0129
1.4 2776 0.0105
1.4 4164 0.0089
1.4 6246 0.0075
1.4 9369 0.0063
1.5 10 0.3797
1.5 15 0.2191
1.5 22 0.1652
1.5 33 0.1311
1.5 49 0.1029
1.5 73 0.0803
1.5 109 0.0648
1.5 163 0.0532
1.5 244 0.0412
1.5 366 0.0348
1.5 549 0.0286
1.5 823 0.0232
1.5 1234 0.0190
1.5 1851 0.0155
1.5 2776 0.0128
1.5 4164 0.0105
1.5 6246 0.0087
1.5 9369 0.0074
1.6 10 0.4158
1.6 15 0.2795
1.6 22 0.1989
1.6 33 0.1519
1.6 49 0.1231
1.6 73 0.0983
1.6 109 0.0765
1.6 163 0.0634
1.6 244 0.0517
1.6 366 0.0422
1.6 549 0.0343
1.6 823 0.0277
1.6 1234 0.0220
1.6 1851 0.0185
1.6 2776 0.0154
1.6 4164 0.0128
1.6 6246 0.0105
1.6 9369 0.0087
1.7 10 0.4748
1.7 15 0.3351
1.7 22 0.2515
1.7 33 0.1800
1.7 49 0.1450
1.7 73 0.1151
1.7 109 0.0922
1.7 163 0.0758
1.7 244 0.0610
1.7 366 0.0487
1.7 549 0.0403
1.7 823 0.0324
1.7 1234 0.0273
1.7 1851 0.0217
1.7 2776 0.0179
1.7 4164 0.0146
1.7 6246 0.0122
1.7 9369 0.0101
1.8 10 0.7570
1.8 15 0.4106
1.8 22 0.2933
1.8 33 0.2153
1.8 49 0.1721
1.8 73 0.1372
1.8 109 0.1113
1.8 163 0.0879
1.8 244 0.0709
1.8 366 0.0581
1.8 549 0.0462
1.8 823 0.0373
1.8 1234 0.0311
1.8 1851 0.0252
1.8 2776 0.0212
1.8 4164 0.0169
1.8 6246 0.0143
1.8 9369 0.0117
1.9 10 0.7859
1.9 15 0.4789
1.9 22 0.3405
1.9 33 0.2507
1.9 49 0.1962
1.9 73 0.1543
1.9 109 0.1265
1.9 163 0.1026
1.9 244 0.0831
1.9 366 0.0677
1.9 549 0.0525
1.9 823 0.0446
1.9 1234 0.0363
1.9 1851 0.0291
1.9 2776 0.0240
1.9 4164 0.0196
1.9 6246 0.0159
1.9 9369 0.0131
2.0 10 0.9426
2.0 15 0.5394
2.0 22 0.3925
2.0 33 0.2953
2.0 49 0.2260
2.0 73 0.1794
2.0 109 0.1437
2.0 163 0.1143
2.0 244 0.0916
2.0 366 0.0745
2.0 549 0.0605
2.0 823 0.0508
2.0 1234 0.0415
2.0 1851 0.0343
2.0 2776 0.0264
2.0 4164 0.0220
2.0 6246 0.0181
2.0 9369 0.0151
2.1 10 1.0576
2.1 15 0.6859
2.1 22 0.4841
2.1 33 0.3391
2.1 49 0.2495
2.1 73 0.1994
2.1 109 0.1623
2.1 163 0.1300
2.1 244 0.1056
2.1 366 0.0855
2.1 549 0.0702
2.1 823 0.0575
2.1 1234 0.0462
2.1 1851 0.0367
2.1 2776 0.0307
2.1 4164 0.0250
2.1 6246 0.0205
2.1 9369 0.0172
2.2 10 1.3051
2.2 15 0.8049
2.2 22 0.5475
2.2 33 0.3760
2.2 49 0.2881
2.2 73 0.2216
2.2 109 0.1807
2.2 163 0.1417
2.2 244 0.1166
2.2 366 0.0960
2.2 549 0.0773
2.2 823 0.0613
2.2 1234 0.0518
2.2 1851 0.0417
2.2 2776 0.0336
2.2 4164 0.0277
2.2 6246 0.0233
2.2 9369 0.0184
2.3 10 1.4063
2.3 15 0.8691
2.3 22 0.5672
2.3 33 0.4405
2.3 49 0.3194
2.3 73 0.2562
2.3 109 0.1917
2.3 163 0.1561
2.3 244 0.1315
2.3 366 0.1030
2.3 549 0.0839
2.3 823 0.0691
2.3 1234 0.0569
2.3 1851 0.0460
2.3 2776 0.0381
2.3 4164 0.0310
2.3 6246 0.0253
2.3 9369 0.0204
2.4 10 1.6058
2.4 15 0.9451
2.4 22 0.7202
2.4 33 0.4594
2.4 49 0.3578
2.4 73 0.2788
2.4 109 0.2208
2.4 163 0.1804
2.4 244 0.1419
2.4 366 0.1167
2.4 549 0.0935
2.4 823 0.0773
2.4 1234 0.0622
2.4 1851 0.0510
2.4 2776 0.0421
2.4 4164 0.0331
2.4 6246 0.0279
2.4 9369 0.0227
2.5 10 1.7511
2.5 15 1.1037
2.5 22 0.7682
2.5 33 0.5032
2.5 49 0.4164
2.5 73 0.3117
2.5 109 0.2397
2.5 163 0.1940
2.5 244 0.1581
2.5 366 0.1268
2.5 549 0.1017
2.5 823 0.0817
2.5 1234 0.0688
2.5 1851 0.0552
2.5 2776 0.0460
2.5 4164 0.0370
2.5 6246 0.0306
2.5 9369 0.0246
2.6 10 1.8867
2.6 15 1.2848
2.6 22 0.8495
2.6 33 0.5802
2.6 49 0.4256
2.6 73 0.3307
2.6 109 0.2653
2.6 163 0.2153
2.6 244 0.1693
2.6 366 0.1394
2.6 549 0.1117
2.6 823 0.0908
2.6 1234 0.0738
2.6 1851 0.0604
2.6 2776 0.0503
2.6 4164 0.0389
2.6 6246 0.0328
2.6 9369 0.0265
2.7 10 1.9545
2.7 15 1.2612
2.7 22 0.9332
2.7 33 0.6492
2.7 49 0.4506
2.7 73 0.3708
2.7 109 0.2924
2.7 163 0.2325
2.7 244 0.1815
2.7 366 0.1521
2.7 549 0.1210
2.7 823 0.0995
2.7 1234 0.0793
2.7 1851 0.0652
2.7 2776 0.0535
2.7 4164 0.0431
2.7 6246 0.0345
2.7 9369 0.0294
2.8 10 2.0765
2.8 15 1.4198
2.8 22 1.0040
2.8 33 0.6910
2.8 49 0.5177
2.8 73 0.3768
2.8 109 0.3186
2.8 163 0.2487
2.8 244 0.1968
2.8 366 0.1637
2.8 549 0.1311
2.8 823 0.1075
2.8 1234 0.0862
2.8 1851 0.0724
2.8 2776 0.0569
2.8 4164 0.0474
2.8 6246 0.0380
2.8 9369 0.0314
2.9 10 2.1684
2.9 15 1.5196
2.9 22 1.1313
2.9 33 0.7469
2.9 49 0.5539
2.9 73 0.4115
2.9 109 0.3304
2.9 163 0.2764
2.9 244 0.2179
2.9 366 0.1748
2.9 549 0.1387
2.9 823 0.1143
2.9 1234 0.0946
2.9 1851 0.0735
2.9 2776 0.0619
2.9 4164 0.0502
2.9 6246 0.0415
2.9 9369 0.0338
3.0 10 2.3521
3.0 15 1.6551
3.0 22 1.1847
3.0 33 0.8477
3.0 49 0.6045
3.0 73 0.4583
3.0 109 0.3655
3.0 163 0.2855
3.0 244 0.2229
3.0 366 0.1813
3.0 549 0.1546
3.0 823 0.1193
3.0 1234 0.1015
3.0 1851 0.0793
3.0 2776 0.0674
3.0 4164 0.0538
3.0 6246 0.0445
3.0 9369 0.0362
3.1 10 2.4406
3.1 15 1.6993
3.1 22 1.2774
3.1 33 0.8406
3.1 49 0.6608
3.1 73 0.4990
3.1 109 0.3851
3.1 163 0.3069
3.1 244 0.2523
3.1 366 0.2027
3.1 549 0.1596
3.1 823 0.1331
3.1 1234 0.1080
3.1 1851 0.0864
3.1 2776 0.0703
3.1 4164 0.0580
3.1 6246 0.0472
3.1 9369 0.0389
3.2 10 2.4487
3.2 15 1.8306
3.2 22 1.3785
3.2 33 0.9406
3.2 49 0.6684
3.2 73 0.5125
3.2 109 0.4177
3.2 163 0.3253
3.2 244 0.2664
3.2 366 0.2126
3.2 549 0.1723
3.2 823 0.1394
3.2 1234 0.1155
3.2 1851 0.0923
3.2 2776 0.0757
3.2 4164 0.0625
3.2 6246 0.0505
3.2 9369 0.0416
3.3 10 2.6408
3.3 15 1.9145
3.3 22 1.4870
3.3 33 0.9752
3.3 49 0.7453
3.3 73 0.5414
3.3 109 0.4412
3.3 163 0.3611
3.3 244 0.2834
3.3 366 0.2269
3.3 549 0.1780
3.3 823 0.1511
3.3 1234 0.1208
3.3 1851 0.1001
3.3 2776 0.0811
3.3 4164 0.0656
3.3 6246 0.0543
3.3 9369 0.0439
3.4 10 2.7294
3.4 15 1.9021
3.4 22 1.4954
3.4 33 1.0699
3.4 49 0.8411
3.4 73 0.5878
3.4 109 0.4560
3.4 163 0.3709
3.4 244 0.3011
3.4 366 0.2431
3.4 549 0.1923
3.4 823 0.1558
3.4 1234 0.1300
3.4 1851 0.1069
3.4 2776 0.0854
3.4 4164 0.0710
3.4 6246 0.0574
3.4 9369 0.0467
3.5 10 2.7236
3.5 15 2.0063
3.5 22 1.5802
3.5 33 1.1844
3.5 49 0.8534
3.5 73 0.6348
3.5 109 0.5018
3.5 163 0.3957
3.5 244 0.3187
3.5 366 0.2529
3.5 549 0.2074
3.5 823 0.1651
3.5 1234 0.1374
3.5 1851 0.1100
3.5 2776 0.0929
3.5 4164 0.0751
3.5 6246 0.0606
3.5 9369 0.0500
3.6 10 2.7921
3.6 15 2.0654
3.6 22 1.6467
3.6 33 1.2926
3.6 49 0.8940
3.6 73 0.6895
3.6 109 0.5315
3.6 163 0.4143
3.6 244 0.3367
3.6 366 0.2672
3.6 549 0.2132
3.6 823 0.1753
3.6 1234 0.1418
3.6 1851 0.1191
3.6 2776 0.0946
3.6 4164 0.0779
3.6 6246 0.0626
3.6 9369 0.0530
3.7 10 2.9026
3.7 15 2.0774
3.7 22 1.7123
3.7 33 1.2821
3.7 49 0.9483
3.7 73 0.7012
3.7 109 0.5592
3.7 163 0.4455
3.7 244 0.3457
3.7 366 0.2844
3.7 549 0.2344
3.7 823 0.1874
3.7 1234 0.1487
3.7 1851 0.1250
3.7 2776 0.1017
3.7 4164 0.0829
3.7 6246 0.0683
3.7 9369 0.0543
3.8 10 2.9733
3.8 15 2.1851
3.8 22 1.7568
3.8 33 1.3959
3.8 49 1.0410
3.8 73 0.7619
3.8 109 0.5795
3.8 163 0.4522
3.8 244 0.3684
3.8 366 0.2974
3.8 549 0.2387
3.8 823 0.1949
3.8 1234 0.1572
3.8 1851 0.1271
3.8 2776 0.1089
3.8 4164 0.0863
3.8 6246 0.0706
3.8 9369 0.0566
3.9 10 2.9475
3.9 15 2.2432
3.9 22 1.8934
3.9 33 1.4587
3.9 49 1.0837
3.9 73 0.8018
3.9 109 0.6271
3.9 163 0.4855
3.9 244 0.3977
3.9 366 0.3146
3.9 549 0.2503
3.9 823 0.2073
3.9 1234 0.1688
3.9 1851 0.1344
3.9 2776 0.1137
3.9 4164 0.0904
3.9 6246 0.0739
3.9 9369 0.0600
4.0 10 2.9829
4.0 15 2.3308
4.0 22 1.9464
4.0 33 1.4693
4.0 49 1.1255
4.0 73 0.8313
4.0 109 0.6538
4.0 163 0.5210
4.0 244 0.4104
4.0 366 0.3267
4.0 549 0.2661
4.0 823 0.2172
4.0 1234 0.1750
4.0 1851 0.1418
4.0 2776 0.1182
4.0 4164 0.0955
4.0 6246 0.0786
4.0 9369 0.0636
Hope this helps,
Rainer
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