-4

使用以下数据： 

time_stamp,secs,count
2013-04-30 23:58:55,1367366335,32
2013-04-30 23:58:56,1367366336,281
2013-04-30 23:58:57,1367366337,664
2013-04-30 23:58:58,1367366338,1255
2013-04-30 23:58:59,1367366339,2011
2013-04-30 23:59:00,1367366340,2819
2013-04-30 23:59:01,1367366341,3489
2013-04-30 23:59:02,1367366342,4230
2013-04-30 23:59:03,1367366343,4892
2013-04-30 23:59:04,1367366344,5185
2013-04-30 23:59:05,1367366345,5415
2013-04-30 23:59:06,1367366346,5428
2013-04-30 23:59:07,1367366347,5255
2013-04-30 23:59:08,1367366348,4897
2013-04-30 23:59:09,1367366349,4548
2013-04-30 23:59:10,1367366350,4154
2013-04-30 23:59:11,1367366351,3718
2013-04-30 23:59:12,1367366352,3521
2013-04-30 23:59:13,1367366353,3193
2013-04-30 23:59:14,1367366354,3015
2013-04-30 23:59:15,1367366355,2722
2013-04-30 23:59:16,1367366356,2545
2013-04-30 23:59:17,1367366357,2368
2013-04-30 23:59:18,1367366358,2265
2013-04-30 23:59:19,1367366359,2162
2013-04-30 23:59:20,1367366360,1967
2013-04-30 23:59:21,1367366361,1952
2013-04-30 23:59:22,1367366362,1750
2013-04-30 23:59:23,1367366363,1720
2013-04-30 23:59:24,1367366364,1624
2013-04-30 23:59:25,1367366365,1497
2013-04-30 23:59:26,1367366366,1452
2013-04-30 23:59:27,1367366367,1486
2013-04-30 23:59:28,1367366368,1328
2013-04-30 23:59:29,1367366369,1284
2013-04-30 23:59:30,1367366370,1266
2013-04-30 23:59:31,1367366371,1220
2013-04-30 23:59:32,1367366372,1152
2013-04-30 23:59:33,1367366373,1217
2013-04-30 23:59:34,1367366374,1144
2013-04-30 23:59:35,1367366375,1113
2013-04-30 23:59:36,1367366376,1051
2013-04-30 23:59:37,1367366377,1036
2013-04-30 23:59:38,1367366378,976
2013-04-30 23:59:39,1367366379,1018
2013-04-30 23:59:40,1367366380,974
2013-04-30 23:59:41,1367366381,946
2013-04-30 23:59:42,1367366382,910
2013-04-30 23:59:43,1367366383,912
2013-04-30 23:59:44,1367366384,853
2013-04-30 23:59:45,1367366385,824
2013-04-30 23:59:46,1367366386,908
2013-04-30 23:59:47,1367366387,800
2013-04-30 23:59:48,1367366388,841
2013-04-30 23:59:49,1367366389,828
2013-04-30 23:59:50,1367366390,775
2013-04-30 23:59:51,1367366391,761
2013-04-30 23:59:52,1367366392,827
2013-04-30 23:59:53,1367366393,725
2013-04-30 23:59:54,1367366394,752
2013-04-30 23:59:55,1367366395,730
2013-04-30 23:59:56,1367366396,701
2013-04-30 23:59:57,1367366397,685
2013-04-30 23:59:58,1367366398,680
2013-04-30 23:59:59,1367366399,704
2013-05-01 00:00:00,1367366400,642
2013-05-01 00:00:01,1367366401,688
2013-05-01 00:00:02,1367366402,682
2013-05-01 00:00:03,1367366403,660
2013-05-01 00:00:04,1367366404,602
2013-05-01 00:00:05,1367366405,672
2013-05-01 00:00:06,1367366406,663
2013-05-01 00:00:07,1367366407,649
2013-05-01 00:00:08,1367366408,609
2013-05-01 00:00:09,1367366409,594
2013-05-01 00:00:10,1367366410,554
2013-05-01 00:00:11,1367366411,554
2013-05-01 00:00:12,1367366412,594
2013-05-01 00:00:13,1367366413,552
2013-05-01 00:00:14,1367366414,565
2013-05-01 00:00:15,1367366415,553
2013-05-01 00:00:16,1367366416,550
2013-05-01 00:00:17,1367366417,513
2013-05-01 00:00:18,1367366418,525
2013-05-01 00:00:19,1367366419,518
2013-05-01 00:00:20,1367366420,485
2013-05-01 00:00:21,1367366421,554
2013-05-01 00:00:22,1367366422,527
2013-05-01 00:00:23,1367366423,490
2013-05-01 00:00:24,1367366424,509
2013-05-01 00:00:25,1367366425,460
2013-05-01 00:00:26,1367366426,473
2013-05-01 00:00:27,1367366427,491
2013-05-01 00:00:28,1367366428,511
2013-05-01 00:00:29,1367366429,490
2013-05-01 00:00:30,1367366430,438
2013-05-01 00:00:31,1367366431,487
2013-05-01 00:00:32,1367366432,449
2013-05-01 00:00:33,1367366433,426
2013-05-01 00:00:34,1367366434,482
2013-05-01 00:00:35,1367366435,484
2013-05-01 00:00:36,1367366436,433
2013-05-01 00:00:37,1367366437,455
2013-05-01 00:00:38,1367366438,441
2013-05-01 00:00:39,1367366439,450
2013-05-01 00:00:40,1367366440,440
2013-05-01 00:00:41,1367366441,446
2013-05-01 00:00:42,1367366442,470
2013-05-01 00:00:43,1367366443,421
2013-05-01 00:00:44,1367366444,456
2013-05-01 00:00:45,1367366445,442
2013-05-01 00:00:46,1367366446,424
2013-05-01 00:00:47,1367366447,416
2013-05-01 00:00:48,1367366448,455
2013-05-01 00:00:49,1367366449,366
2013-05-01 00:00:50,1367366450,407
2013-05-01 00:00:51,1367366451,413
2013-05-01 00:00:52,1367366452,420
2013-05-01 00:00:53,1367366453,396
2013-05-01 00:00:54,1367366454,428
2013-05-01 00:00:55,1367366455,344
2013-05-01 00:00:56,1367366456,372
2013-05-01 00:00:57,1367366457,388
2013-05-01 00:00:58,1367366458,394
2013-05-01 00:00:59,1367366459,383
2013-05-01 00:01:00,1367366460,391
2013-05-01 00:01:01,1367366461,385
2013-05-01 00:01:02,1367366462,410
2013-05-01 00:01:03,1367366463,359
2013-05-01 00:01:04,1367366464,328
2013-05-01 00:01:05,1367366465,396
2013-05-01 00:01:06,1367366466,388
2013-05-01 00:01:07,1367366467,402
2013-05-01 00:01:08,1367366468,349
2013-05-01 00:01:09,1367366469,355
2013-05-01 00:01:10,1367366470,315
2013-05-01 00:01:11,1367366471,360
2013-05-01 00:01:12,1367366472,357
2013-05-01 00:01:13,1367366473,369
2013-05-01 00:01:14,1367366474,337
2013-05-01 00:01:15,1367366475,358
2013-05-01 00:01:16,1367366476,367
2013-05-01 00:01:17,1367366477,357
2013-05-01 00:01:18,1367366478,362
2013-05-01 00:01:19,1367366479,302
2013-05-01 00:01:20,1367366480,346
2013-05-01 00:01:21,1367366481,338
2013-05-01 00:01:22,1367366482,366
2013-05-01 00:01:23,1367366483,341
2013-05-01 00:01:24,1367366484,332
2013-05-01 00:01:25,1367366485,317
2013-05-01 00:01:26,1367366486,310
2013-05-01 00:01:27,1367366487,327
2013-05-01 00:01:28,1367366488,333
2013-05-01 00:01:29,1367366489,322
2013-05-01 00:01:30,1367366490,344
2013-05-01 00:01:31,1367366491,330
2013-05-01 00:01:32,1367366492,312
2013-05-01 00:01:33,1367366493,292
2013-05-01 00:01:34,1367366494,315
2013-05-01 00:01:35,1367366495,326
2013-05-01 00:01:36,1367366496,313
2013-05-01 00:01:37,1367366497,307
2013-05-01 00:01:38,1367366498,325
2013-05-01 00:01:39,1367366499,308
2013-05-01 00:01:40,1367366500,299
2013-05-01 00:01:41,1367366501,293
2013-05-01 00:01:42,1367366502,285
2013-05-01 00:01:43,1367366503,295
2013-05-01 00:01:44,1367366504,310
2013-05-01 00:01:45,1367366505,309
2013-05-01 00:01:46,1367366506,289
2013-05-01 00:01:47,1367366507,307
2013-05-01 00:01:48,1367366508,311
2013-05-01 00:01:49,1367366509,294
2013-05-01 00:01:50,1367366510,279
2013-05-01 00:01:51,1367366511,280
2013-05-01 00:01:52,1367366512,247
2013-05-01 00:01:53,1367366513,285
2013-05-01 00:01:54,1367366514,288
2013-05-01 00:01:55,1367366515,250
2013-05-01 00:01:56,1367366516,284
2013-05-01 00:01:57,1367366517,281
2013-05-01 00:01:58,1367366518,250
2013-05-01 00:01:59,1367366519,266
2013-05-01 00:02:00,1367366520,305
2013-05-01 00:02:01,1367366521,257
2013-05-01 00:02:02,1367366522,252
2013-05-01 00:02:03,1367366523,261
2013-05-01 00:02:04,1367366524,253
2013-05-01 00:02:05,1367366525,273
2013-05-01 00:02:06,1367366526,290
2013-05-01 00:02:07,1367366527,267
2013-05-01 00:02:08,1367366528,289
2013-05-01 00:02:09,1367366529,259
2013-05-01 00:02:10,1367366530,281
2013-05-01 00:02:11,1367366531,242
2013-05-01 00:02:12,1367366532,280
2013-05-01 00:02:13,1367366533,300
2013-05-01 00:02:14,1367366534,284
2013-05-01 00:02:15,1367366535,244
2013-05-01 00:02:16,1367366536,236
2013-05-01 00:02:17,1367366537,269
2013-05-01 00:02:18,1367366538,292
2013-05-01 00:02:19,1367366539,279
2013-05-01 00:02:20,1367366540,234
2013-05-01 00:02:21,1367366541,262
2013-05-01 00:02:22,1367366542,245
2013-05-01 00:02:23,1367366543,258
2013-05-01 00:02:24,1367366544,230
2013-05-01 00:02:25,1367366545,252
2013-05-01 00:02:26,1367366546,273
2013-05-01 00:02:27,1367366547,216
2013-05-01 00:02:28,1367366548,245
2013-05-01 00:02:29,1367366549,254
2013-05-01 00:02:30,1367366550,293
2013-05-01 00:02:31,1367366551,331
2013-05-01 00:02:32,1367366552,320
2013-05-01 00:02:33,1367366553,303
2013-05-01 00:02:34,1367366554,378
2013-05-01 00:02:35,1367366555,348
2013-05-01 00:02:36,1367366556,347
2013-05-01 00:02:37,1367366557,316
2013-05-01 00:02:38,1367366558,333
2013-05-01 00:02:39,1367366559,299
2013-05-01 00:02:40,1367366560,284
2013-05-01 00:02:41,1367366561,279
2013-05-01 00:02:42,1367366562,261
2013-05-01 00:02:43,1367366563,259
2013-05-01 00:02:44,1367366564,223
2013-05-01 00:02:45,1367366565,229
2013-05-01 00:02:46,1367366566,243
2013-05-01 00:02:47,1367366567,217
2013-05-01 00:02:48,1367366568,225
2013-05-01 00:02:49,1367366569,215
2013-05-01 00:02:50,1367366570,265
2013-05-01 00:02:51,1367366571,240
2013-05-01 00:02:52,1367366572,248
2013-05-01 00:02:53,1367366573,226
2013-05-01 00:02:54,1367366574,188
2013-05-01 00:02:55,1367366575,213
2013-05-01 00:02:56,1367366576,216
2013-05-01 00:02:57,1367366577,222
2013-05-01 00:02:58,1367366578,282
2013-05-01 00:02:59,1367366579,234
2013-05-01 00:03:00,1367366580,216
2013-05-01 00:03:01,1367366581,195
2013-05-01 00:03:02,1367366582,224
2013-05-01 00:03:03,1367366583,227
2013-05-01 00:03:04,1367366584,256
2013-05-01 00:03:05,1367366585,213
2013-05-01 00:03:06,1367366586,225
2013-05-01 00:03:07,1367366587,229
2013-05-01 00:03:08,1367366588,217
2013-05-01 00:03:09,1367366589,220
2013-05-01 00:03:10,1367366590,209
2013-05-01 00:03:11,1367366591,231
2013-05-01 00:03:12,1367366592,195
2013-05-01 00:03:13,1367366593,231
2013-05-01 00:03:14,1367366594,185
2013-05-01 00:03:15,1367366595,173
2013-05-01 00:03:16,1367366596,190
2013-05-01 00:03:17,1367366597,196
2013-05-01 00:03:18,1367366598,190
2013-05-01 00:03:19,1367366599,209
2013-05-01 00:03:20,1367366600,206
2013-05-01 00:03:21,1367366601,227
2013-05-01 00:03:22,1367366602,199
2013-05-01 00:03:23,1367366603,182
2013-05-01 00:03:24,1367366604,202
2013-05-01 00:03:25,1367366605,208
2013-05-01 00:03:26,1367366606,190
2013-05-01 00:03:27,1367366607,220
2013-05-01 00:03:28,1367366608,190
2013-05-01 00:03:29,1367366609,205
2013-05-01 00:03:30,1367366610,196
2013-05-01 00:03:31,1367366611,182
2013-05-01 00:03:32,1367366612,187
2013-05-01 00:03:33,1367366613,186
2013-05-01 00:03:34,1367366614,195
2013-05-01 00:03:35,1367366615,224
2013-05-01 00:03:36,1367366616,210
2013-05-01 00:03:37,1367366617,188
2013-05-01 00:03:38,1367366618,167
2013-05-01 00:03:39,1367366619,194
2013-05-01 00:03:40,1367366620,187
2013-05-01 00:03:41,1367366621,213
2013-05-01 00:03:42,1367366622,193
2013-05-01 00:03:43,1367366623,187
2013-05-01 00:03:44,1367366624,209
2013-05-01 00:03:45,1367366625,204
2013-05-01 00:03:46,1367366626,199
2013-05-01 00:03:47,1367366627,186
2013-05-01 00:03:48,1367366628,197
2013-05-01 00:03:49,1367366629,196
2013-05-01 00:03:50,1367366630,182
2013-05-01 00:03:51,1367366631,169
2013-05-01 00:03:52,1367366632,196
2013-05-01 00:03:53,1367366633,198
2013-05-01 00:03:54,1367366634,187
2013-05-01 00:03:55,1367366635,178
2013-05-01 00:03:56,1367366636,197
2013-05-01 00:03:57,1367366637,172
2013-05-01 00:03:58,1367366638,186
2013-05-01 00:03:59,1367366639,181
2013-05-01 00:04:00,1367366640,167
2013-05-01 00:04:01,1367366641,201
2013-05-01 00:04:02,1367366642,172
2013-05-01 00:04:03,1367366643,190
2013-05-01 00:04:04,1367366644,167
2013-05-01 00:04:05,1367366645,152
2013-05-01 00:04:06,1367366646,186
2013-05-01 00:04:07,1367366647,193
2013-05-01 00:04:08,1367366648,207
2013-05-01 00:04:09,1367366649,182
2013-05-01 00:04:10,1367366650,182
2013-05-01 00:04:11,1367366651,183
2013-05-01 00:04:12,1367366652,204
2013-05-01 00:04:13,1367366653,163
2013-05-01 00:04:14,1367366654,164
2013-05-01 00:04:15,1367366655,156
2013-05-01 00:04:16,1367366656,177
2013-05-01 00:04:17,1367366657,162
2013-05-01 00:04:18,1367366658,168
2013-05-01 00:04:19,1367366659,178
2013-05-01 00:04:20,1367366660,201
2013-05-01 00:04:21,1367366661,165
2013-05-01 00:04:22,1367366662,181
2013-05-01 00:04:23,1367366663,152
2013-05-01 00:04:24,1367366664,160
2013-05-01 00:04:25,1367366665,169
2013-05-01 00:04:26,1367366666,149
2013-05-01 00:04:27,1367366667,146
2013-05-01 00:04:28,1367366668,165
2013-05-01 00:04:29,1367366669,179
2013-05-01 00:04:30,1367366670,164
2013-05-01 00:04:31,1367366671,205
2013-05-01 00:04:32,1367366672,144
2013-05-01 00:04:33,1367366673,165
2013-05-01 00:04:34,1367366674,155
2013-05-01 00:04:35,1367366675,178
2013-05-01 00:04:36,1367366676,185
2013-05-01 00:04:37,1367366677,170
2013-05-01 00:04:38,1367366678,160
2013-05-01 00:04:39,1367366679,162
2013-05-01 00:04:40,1367366680,154
2013-05-01 00:04:41,1367366681,151
2013-05-01 00:04:42,1367366682,157
2013-05-01 00:04:43,1367366683,138
2013-05-01 00:04:44,1367366684,166
2013-05-01 00:04:45,1367366685,156
2013-05-01 00:04:46,1367366686,180
2013-05-01 00:04:47,1367366687,157
2013-05-01 00:04:48,1367366688,142
2013-05-01 00:04:49,1367366689,142
2013-05-01 00:04:50,1367366690,168
2013-05-01 00:04:51,1367366691,167
2013-05-01 00:04:52,1367366692,159
2013-05-01 00:04:53,1367366693,172
2013-05-01 00:04:54,1367366694,142
2013-05-01 00:04:55,1367366695,156
2013-05-01 00:04:56,1367366696,165
2013-05-01 00:04:57,1367366697,163
2013-05-01 00:04:58,1367366698,162
2013-05-01 00:04:59,1367366699,135

您将如何仅使用该数据的前 30 秒来计算拟合的伽马值？这里的目标是绘制随时间变化的计数，然后通过数据绘制拟合曲线。

4

2 回答 2

2

-1 给 OP 没有显示工作，但 +1 发布一个有趣的问题。这是一个尝试。这个想法是将曲线拟合到（x，y）数据，其中曲线是（缩放的）伽马密度。由于数据是网格上的计数表，泊松误差分布似乎是一个合理的假设。我隐含地重新调整了问题的大小，使网格为 1...365 而不是 1367366395...1367366699 以使生活更轻松；将结果转换回原始量表是读者的练习。

negll <- function(par, x, y)
{
    shape <- par[1]
    rate <- par[2]
    mu <- dgamma(x, shape, rate) * sum(y)
    -2 * sum(dpois(y, mu, log=TRUE))
}


optim(c(1, 1), negll, x=seq_along(g$count), y=g$count, method="L-BFGS-B", lower=c(.001, .001))
$par
[1] 0.73034879 0.00698288

$value
[1] 62983.18

$counts
function gradient 
      32       32 

$convergence
[1] 0

$message
[1] "CONVERGENCE: REL_REDUCTION_OF_F <= FACTR*EPSMCH"

这实际上是一个非常差的拟合（shape与观察到的数据相比，小于 1 表示拟合曲线在原点处趋于无穷大）。从观察到的趋势来看，伽马密度对于该数据来说是一个糟糕的选择；峰太尖，衰减太慢。像（广义）帕累托这样的重尾分布可能是更好的选择。

再加上一些东西：

  1. 这适合整个表格，而不仅仅是前 30 个点。仅使用 30 个点会使其变得更加困难，因为仅从曲线的那一部分您就可以获得关于形状和速率的最少信息。

  2. 在向下 2/3 处的曲线上有一个明显的颠簸。这是否重要由 OP 决定，但我希望他们真正注意到这一点，而不是直接跳到曲线拟合阶段。

于 2013-06-21T04:44:14.300 回答
0

我会在拟合之前可视化我的分布：

 library(latticeExtra)  ## useful for zoo objects
 ## plotting 30 points don't give a gamma like plot...
 ## but 100 points is better
 marginal.plot(dat$count[1:100])

在此处输入图像描述

然后使用fitdistrfromMASS

## Normalize to avoid bad minima
xx <- as.numeric(dat[1:100,'count'])/max(dat$count)
fitdistr(xx,'gamma',  start=list(shape = 2, rate = 0.1),lower=0.00001)
     shape       rate   
  1.6190036   6.1598943 
 (0.2096129) (0.9329586)
于 2013-06-21T00:36:52.440 回答