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缘牵一线624

木虫 (小有名气)

[求助] 求教大神们:离散随机变量的概率密度的求法? 已有1人参与

问题:
我在统计某一生物细胞的尺寸,统计总体大约为九百多个,得到一系列离散数据,那么如何根据这组数据得出其概率密度呢?
例如:这组数据如下
x=[7.164700491
7.640463854
7.799701938
7.941122713
8.022293777
8.121084064
8.180192015
8.244923163
8.287128382
8.303149583
8.426283946
8.445974807
8.487180291
8.539865301
8.568996849
8.588360513
8.711278289
8.871894361
9.088335073
9.155717646
9.188319919
9.200967998
9.480198942
9.615910382
9.631445646
9.641789682
9.659004577
9.727557873
9.787147103
9.795631419
9.834559821
9.963779947
10.12749663
10.21731701
10.22869263
10.28860912
10.35620372
10.38823594
10.39303264
10.43132531
10.43928457
10.44723777
10.6034936
10.66130422
10.70174103
10.7157037
10.72500056
10.79293972
10.829817
10.84667902
10.97306343
11.12939958
11.16367945
11.19933602
11.19933602
11.31444598
11.34084411
11.35840832
11.37156472
11.41530708
11.56279312
11.61869101
11.64725303
11.66293192
11.66293192
11.72260324
11.75656613
11.78620185
11.81435891
11.89563427
11.89703169
11.94719406
11.99991773
12.07994469
12.16081207
12.19219234
12.22620788
12.24928569
12.26554908
12.32230333
12.33712485
12.35461697
12.36939927
12.37879711
12.45505806
12.47771134
12.50696748
12.54940047
12.55734033
12.62331404
12.63120819
12.66666848
12.67191337
12.68632596
12.69679733
12.79195483
12.79844736
12.80493535
12.80752914
12.8580169
12.92631124
12.99808168
13.04783214
13.05165143
13.06691621
13.06818839
13.11893779
13.16065963
13.1707551
13.19595697
13.19721549
13.21734168
13.26000644
13.26125889
13.27127663
13.39090741
13.41569691
13.46637118
13.48855731
13.55612654
13.58183735
13.59284071
13.60872016
13.65016157
13.69633011
13.70481807
13.713301
13.73387995
13.76891403
13.8170911
13.85910793
13.88066749
13.92726556
13.99746337
14.00458296
14.0306557
14.07085573
14.10151774
14.12976373
14.18374305
14.22351041
14.2771353
14.27829853
14.3571982
14.37569937
14.38378643
14.41724165
14.45406738
14.46670458
14.46900047
14.54343922
14.57652768
14.58792036
14.59247472
14.60271657
14.73747444
14.8083188
14.86318819
14.86430555
14.95344793
14.96677318
14.98673936
15.02327494
15.26678673
15.26787456
15.30482418
15.31350617
15.34493319
15.34601652
15.3525097
15.5578139
15.58874941
15.61324054
15.61536888
15.62175113
15.62919345
15.64194304
15.7498994
15.77414033
15.82461096
15.86654735
15.86864171
15.89061134
15.90628406
15.92820276
15.96882612
15.97402749
15.98961845
16.10453115
16.11793518
16.17349704
16.18684494
16.22374901
16.25750488
16.29934644
16.36850664
16.37662424
16.40601587
16.41613797
16.43939749
16.45757623
16.47170224
16.50092451
16.54215037
16.54616684
16.57926627
16.58728025
16.70802565
16.74378219
16.75667564
16.76757752
16.81506661
16.93811046
16.9390919
17.03980727
17.06026784
17.07097604
17.11568264
17.19025702
17.20184963
17.21536493
17.23754512
17.28278201
17.33556872
17.34610586
17.36907623
17.41969381
17.48727381
17.55364662
17.55743169
17.63955818
17.65179661
17.68658403
17.70254489
17.72224034
17.78867098
17.81759758
17.8297147
17.89852857
17.95968592
18.12817071
18.16935546
18.19311657
18.29328477
18.32595007
18.3341073
18.35131332
18.38206513
18.38567706
18.45152023
18.54491878
18.69569418
18.75247754
18.75336912
18.7799188
18.7958357
18.90072118
18.91653643
18.94199157
18.94637084
19.03560191
19.08179677
19.12614844
19.17992249
19.19204818
19.25771415
19.26806374
19.28099292
19.36009752
19.3755378
19.48582696
19.50883354
19.57938601
19.6344621
19.81301927
19.85991546
19.91922382
19.92421949
19.97335805
20.10021073
20.10186638
20.18186422
20.21229997
20.27220808
20.43869971
20.49551761
20.52953442
20.54328195
20.5756024
20.59900746
20.62157518
20.64733446
20.65296897
20.65457492
20.7027799
20.74126322
20.74366606
20.7484709
20.77726894
21.02999072
21.10805533
21.18111916
21.27190516
21.48559731
21.53039623
21.53810872
21.55507684
21.62586473
21.62816929
21.71096321
21.7652209
21.89914636
21.9203756
21.97789857
22.03903601
22.04808006
22.09925497
22.20424875
22.27819905
22.28565275
22.30278752
22.36081508
22.37195697
22.44831289
22.52514518
22.75992259
22.78618422
22.95542621
23.00530955
23.05652152
23.08316452
23.16147829
23.22522651
23.27524313
23.29735777
23.3166038
23.33013551
23.33867925
23.37282297
23.38632215
23.43386819
23.45087697
23.64066856
23.67507625
23.68840319
23.71153607
23.73744388
23.96936075
24.02404581
24.06964417
24.08758567
24.11515632
24.12824019
24.15714213
24.18051145
24.37552547
24.48771953
24.49925256
24.54260562
24.55140843
24.55208295
24.57170062
24.61020321
24.6574119
24.72200856
24.73678635
24.74752706
24.86004776
24.87073588
24.93610944
24.96939528
25.03185868
25.12658399
25.18139921
25.21634416
25.23543914
25.25452599
25.51498873
25.69858357
25.77668675
25.89371957
25.89692331
25.95139381
26
26.00447046
26.00830343
26.01724685
26.03064705
26.07145986
26.07210115
26.09375551
26.11284917
26.11411752
26.31121918
26.31311339
26.36798024
26.47612793
26.48051802
26.49368991
26.49368991
26.51186491
26.51875913
26.56006892
26.66743762
26.66992748
26.72779154
27.4029672
27.41387788
27.52515352
27.60771608
27.79004542
27.94266195
27.96643234
28.02280691
28.2053943
28.20598143
28.46978508
28.56008863
28.73059024
28.76353185
28.80220268
28.99707321
29.07659553
29.20372653
29.22022138
29.40893317
29.41570597
29.56049072
29.81844212
29.90800651
29.98567068
30.43111674
30.55913657
30.79362164
30.82004476
30.94162369
31.24084273
31.28441544
31.30777462
31.3448916
32.08244753
32.37420043
32.42137476
32.47922413
32.53646166
32.55738687
32.69689987
32.90859276
33.28354828
33.51929761
33.55892242
33.75093771
33.84433266
33.87131887
34.41528415
34.51939361
34.77256862
34.77591139
34.82698822
34.82985029
35.09546126
35.25791685
35.26451456
35.60021291
35.76595453
35.99559863
36.06752337
36.18019305
36.26274869
36.38897257
36.50611152
36.53249143
36.54431478
36.56521963
36.92194383
36.95117712
37.08088078
37.53728083
37.6133277
37.63451881
37.72446198
37.76143266
37.80320311
37.84273525
37.88924103
37.94269481
38.15706311
38.39057989
38.43339428
38.45759514
38.51069005
38.69359054
38.96398795
39.12354676
39.44029996
39.61429887
39.68594466
39.84761179
40.33367593
40.41678957
40.786264
40.81598444
40.84650076
40.84812636
40.89893206
40.91273921
41.28300648
41.43363583
41.52134744
41.5797216
41.6499784
42.31594089
42.73705339
43.1555954
43.3457243
43.56439702
43.59870199
43.9905498
44.35309969
44.35460036
44.38081082
44.8288536
45.12544793
45.81160187
46.12780984
46.2964107
46.30860859
46.3641808
46.93963463
47.08028108
47.25251316
47.40449668
48.14653522
48.23375275
48.49994419
49.49538999
51.14443766
51.21357802
52.17572892
52.52796344
52.77878965
52.98392978
53.60362308
53.67330998
53.85993276
53.86085517
54.00316398
54.27993318
54.29492475
54.31113949
54.6490016
54.74831818
55.23378512
55.28068505
55.94503672
56.06842953
56.25655517
56.46406895
57.034016
57.13733595
57.36454552
57.41692975
58.39037854
58.57446673
58.58126263
58.72995525
59.14176534
59.1639738
59.25038633
59.31874388
59.84321341
60.09061629
60.45361964
60.48163905
60.77291447
61.18157168
61.21386234
61.34290692
61.39057377
61.58588845
61.73272986
61.73435489
62.0647135
62.06525229
62.13989252
62.20561242
62.41225688
63.01938333
63.24882618
63.87530149
64.08302238
64.63567669
64.94105608
65.77981511
66.25015323
66.46044271
66.61150319
66.78337449
66.92302356
67.2513822
67.6007387
68.18383263
68.59509184
68.77793584
69.07535348
69.3053798
69.30799901
69.34419827
69.43995711
70.28742175
70.36465528
70.37954429
70.4080916
70.68196015
71.54166752
71.93324489
72.23861293
72.37002406
72.79711795
72.89653256
73.03360626
73.07316811
74.04160476
74.15839907
74.16937708
74.31236149
74.44212902
74.52710788
74.73656495
74.88513497
74.89776471
74.99509538
75.05441763
75.09802511
75.53849147
75.54376131
75.77453566
76.32913561
76.36961746
76.43441467
76.51066284
76.66250796
76.85166455
76.89509978
77.09252857
77.37537751
77.58293282
77.66062049
78.41505201
79.56650065
80.40704567
80.53875121
81.04559541
81.14987707
81.56926251
81.81776394
81.83379926
81.91252908
82.10962456
82.53300826
83.03270402
83.19319852
83.51884871
83.66034987
84.04470679
84.37867708
84.46448015
84.54094851
84.7011419
85.17036131
85.24970815
85.40275507
85.60210129
85.80194941
85.85285887
86.05501129
86.27577617
86.63987623
86.67861056
86.92873573
88.31393049
88.51272894
88.58701505
88.61027172
88.63425888
88.82821753
88.93850305
89.16645138
89.34011446
89.79342889
89.89641952
90.00500694
90.04542378
90.71209794
91.04681374
91.22836538
91.35756029
91.42281211
91.42826362
91.4615056
91.90924283
92.05661509
92.14499789
93.44667065
93.62144264
93.83553847
94.09667748
94.45719888
94.57918867
94.87678902
95.30602737
95.44188214
95.58972175
95.60901005
95.7413248
96.06680597
96.53998215
97.12123883
97.18979724
97.39232173
97.67318442
98.98809682
99.08521071
99.36148057
100.4812148
101.0621616
101.2648039
101.3777699
101.9390976
102.0674343
102.8258484
103.0512982
103.1718158
104.5680682
104.8452454
104.8555421
105.0712527
106.0859959
106.2399789
106.4188636
106.631113
106.875128
106.9007665
107.5561178
107.9794154
108.3130489
108.5641523
108.6037764
108.6436939
108.6461416
108.8444224
109.0352015
109.4766066
109.7365403
109.7652968
110.0502202
110.3688748
110.5230471
111.0350263
111.0532666
112.1561128
112.5689032
112.7087306
112.7380426
112.9953356
113.1397591
113.3817743
113.7502572
114.337889
114.4391057
114.6359372
114.6591182
114.6683948
114.6799757
115.037089
115.047913
115.1392815
115.5119317
115.8092546
116.268386
116.8176092
117.3138585
117.5236824
117.6076144
117.7779812
117.7943393
117.8975319
118.162147
118.2217365
118.2615045
119.2254328
119.9717589
119.9979299
120.1246698
120.4932128
120.8952671
121.2914687
122.0485703
122.1726485
122.2690127
122.9791811
123.3404098
123.5788384
123.611769
123.7481133
123.7783102
124.1393556
124.4410177
124.4725176
124.5081534
124.7182557
126.0540401
126.1735106
126.6415021
126.9263666
127.1463122
127.4827077
127.9775931
128.0728296
128.115891
128.3688828
128.5841691
129.0148365
129.0566829
129.9704646
130.0128974
130.154526
130.2193519
130.3373013
130.9830664
131.1651971
131.1786233
132.9037773
133.1255812
133.2539241
134.3084434
134.5407854
134.689369
134.8000761
135.1193858
135.4185538
136.627032
136.7184447
139.3816303
140.0187885
140.0349251
140.2808602
141.8836991
142.1875612
142.7825281
143.1498257
143.481007
143.7524965
143.7761773
144.1174437
145.9782387
146.162134
147.6535798
147.6719121
148.3161325
148.4998231
148.7203741
149.4546882
149.5703507
149.590013
150.6266634
150.8253936
151.0395717
152.6590535
153.0448812
153.129956
153.6188931
153.8911643
154.1135945
154.6857818
155.4812623
155.6339818
156.0029703
156.1866636
156.3643976
156.8404906
157.7603702
158.4699855
158.7956765
159.9698419
160.7191145
161.4880643
161.5294081
165.6936395
165.7165968
166.6460837
174.2490987
175.8195912
178.655096
178.9434669
179.3570435
180.5071588
181.09425
181.3282557
185.0768475
185.1148722
189.3376824
189.8807034
193.6341188
194.5151575
201.4786107
203.1540315
]
求大神指导,给出求解方法或者求解思路哇!   谢谢。。。。
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男儿当自强
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feixiaolin

荣誉版主 (文坛精英)

优秀版主

Minitab中文版有这个功能
2楼2014-12-08 11:15:49
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math2000

铁杆木虫 (职业作家)

【答案】应助回帖

感谢参与,应助指数 +1
1)利用matlab画出直方图,根据其图像,确定分布类型,
2)利用统计的非参数假设检验,看其是否服从1)的分布
3楼2014-12-08 11:54:51
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缘牵一线624

木虫 (小有名气)

引用回帖:
3楼: Originally posted by math2000 at 2014-12-08 11:54:51
1)利用matlab画出直方图,根据其图像,确定分布类型,
2)利用统计的非参数假设检验,看其是否服从1)的分布

非常感谢math2000,我也是画出直方图像,不过很难确定是属于哪种分布形式。
如果无法确定分布形式,可以得出其概率密度吗?   如果可以的话,麻烦帮我把上面的数据给出概率密度。
谢谢
男儿当自强
4楼2014-12-08 18:55:43
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math2000

铁杆木虫 (职业作家)

引用回帖:
4楼: Originally posted by 缘牵一线624 at 2014-12-08 18:55:43
非常感谢math2000,我也是画出直方图像,不过很难确定是属于哪种分布形式。
如果无法确定分布形式,可以得出其概率密度吗?   如果可以的话,麻烦帮我把上面的数据给出概率密度。
谢谢...

你可以根据原始数据的直方图,然后做一个变换,使得变换后数据的直方图是比较熟悉的分布
5楼2014-12-17 11:02:20
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