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有点难度的计算题:Weibull 分布三参数的极大似然估计

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发表于 2020-10-25 00:45 | 显示全部楼层 |阅读模式
本帖最后由 Ysu2008 于 2020-10-25 00:50 编辑

同时估计 Weibull 三参数为啥难?因为很难收敛,牛顿找不到路上山, MATLAB 也只提供两参数的估计工具。离了 MATLAB 这“张屠夫”,难道就不吃猪肉了吗?

以下 30 个样本数据抽取自 weibull 分布, 参数真值为: Shape=2 , Scale=5 , Location=7 ;

用盗版软件上没有的方法估算参数得 Shape=1.771 , Scale=4.638  , Location=7.231 ,还算凑合吧?  

8.621198315460012
13.717089157665308
7.529212937047404
16.82948577020857
7.872675914743467
10.212279065449888
9.464929987790391
9.97499925749947
9.968363015962641
8.971423415115584
12.633767240951785
10.619367457564014
14.960846328203768
11.905634655165914
16.790019552054957
10.085096528120381
11.475542797143076
9.475619106343682
9.71504259660411
12.490799454813754
14.673698918319722
12.85018188442489
10.3379871880727
9.775697130307924
13.524727712596977
10.441080148562722
12.593695175878743
10.621881330585417
13.554847419300055
9.190411699927047
 楼主| 发表于 2020-10-25 00:49 | 显示全部楼层
以下 60 个样本数据也抽取自 Weibull 分布, 参数真值为: Shape=1 , Scale=3 , Location=8 ;

用盗版软件上没有的方法估算参数得 Shape=0.8302 , Scale=2.2662  , Location=8.0157 ,还行吧?

10.010880890059694
9.066228840216404
13.441173715444684
9.73577658861857
10.463478256986722
10.19619926285695
8.084135932382129
12.598404065063253
10.598022248362641
8.959969520187158
12.395827700927022
13.539671303454547
11.936325418467423
8.110402166554227
8.2596497241331
11.342211435996491
8.291028543915877
9.603227324590735
16.33470731717461
8.015695778709214
10.602826427668466
9.676013448050412
11.933287060852761
8.449717814931736
11.878171424938255
10.834576470322636
13.707004665752468
9.735763698271295
13.986302478521662
9.119957586230516
8.21602920106376
12.401376696414104
9.906093204493475
8.36453391478813
9.166656932387571
10.410701734982396
11.150489406271111
15.563551875092417
12.960945498059425
11.47698730052089
8.131179209628836
8.946862675597512
8.115797770928072
13.487443859203392
9.3492044991071
9.691412056835038
11.225980243059112
10.355055901702023
8.824116206418843
8.128600806772205
8.361920362175692
8.028176799670137
9.097483400489358
8.031651985463101
8.567074474742057
9.05405584024431
10.23000488498877
19.482884280771692
9.922987818154786
8.157039051391786
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 楼主| 发表于 2020-10-25 00:53 | 显示全部楼层
感兴趣的朋友可以尝试一下,希望能超过我的估计精度。
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