如何从 R 中的一组观测值生成概率密度分布？
概率密度分布是概率密度函数的同义词。它是一个定义连续随机变量密度的函数。在R中，我们可以使用密度函数从一组观测值中创建概率密度分布。
示例
x1<-c(1,5,2,7,8,2,5) pdf_x1<-density(x1,from=1,to=8) pdf_x1输出结果
Call:
density.default(x = x1, from = 1, to = 8)
Data: x1 (7 obs.); Bandwidth 'bw' = 1.641
x y
Min. :1.00 Min. :0.07678
1st Qu.:2.75 1st Qu.:0.10308
Median :4.50 Median :0.10660
Mean :4.50 Mean :0.10421
3rd Qu.:6.25 3rd Qu.:0.10809
Max. :8.00 Max. :0.11238示例
x2<-sample(0:9,150,replace=TRUE) x2输出结果
[1] 5 0 5 1 7 4 2 0 1 1 4 6 4 9 8 5 3 1 5 7 7 0 6 3 2 0 9 6 1 0 1 3 2 1 7 0 3 [38] 4 2 0 7 1 9 2 0 7 6 7 2 2 2 2 7 0 5 3 8 9 4 0 5 7 2 3 9 7 1 3 5 8 0 1 9 9 [75] 4 1 0 5 2 8 5 8 8 6 0 1 2 6 5 0 5 3 2 0 3 4 9 5 2 4 4 0 7 0 1 1 0 0 8 1 4 [112] 0 8 0 1 4 5 2 1 1 3 3 0 2 5 7 1 6 9 9 8 5 4 1 7 7 9 3 3 2 0 4 2 7 1 6 1 9 [149] 7 4
示例
pdf_x2<-density(x2,from=0,to=9) pdf_x2输出结果
Call:
density.default(x = x2, from = 0, to = 9)
Data: x2 (150 obs.); Bandwidth 'bw' = 0.968
x y
Min. :0.00 Min. :0.05290
1st Qu.:2.25 1st Qu.:0.08010
Median :4.50 Median :0.09063
Mean :4.50 Mean :0.09423
3rd Qu.:6.75 3rd Qu.:0.11063
Max. :9.00 Max. :0.13117示例
x3<-sample(1:100,150,replace=TRUE) x3输出结果
[1] 82 59 78 79 52 1 79 15 53 29 54 65 85 26 41 62 8 33 [19] 91 2 66 59 32 63 84 67 82 13 46 5 11 52 53 12 52 38 [37] 73 10 33 84 67 67 55 92 45 48 54 38 96 69 25 22 64 73 [55] 19 68 87 71 62 91 99 56 81 83 3 32 49 77 14 26 73 60 [73] 80 13 18 97 100 75 45 4 46 33 86 96 23 47 57 48 64 34 [91] 9 90 49 79 20 13 99 7 76 37 91 91 7 98 52 95 17 97 [109] 30 50 63 100 5 47 48 90 3 74 94 78 49 9 19 100 60 13 [127] 27 6 51 8 69 92 28 91 55 89 85 72 17 77 16 52 72 56 [145] 60 70 84 84 12 4
示例
pdf_x3<-density(x3,from=1,to=99) pdf_x3输出结果
Call:
density.default(x = x3, from = 1, to = 99)
Data: x3 (150 obs.); Bandwidth 'bw' = 9.781
x y
Min. : 1.0 Min. :0.005490
1st Qu.:25.5 1st Qu.:0.007753
Median :50.0 Median :0.008883
Mean :50.0 Mean :0.009197
3rd Qu.:74.5 3rd Qu.:0.010991
Max. :99.0 Max. :0.011267示例
x4<-sample(111:999,150,replace=TRUE) x4输出结果
[1] 393 314 643 304 241 512 146 497 563 982 891 732 372 749 718 813 304 994 [19] 760 937 835 182 357 676 111 139 574 293 248 973 700 173 676 636 760 217 [37] 962 265 421 200 245 665 901 294 433 958 277 771 229 306 361 208 346 466 [55] 114 921 816 278 701 543 563 806 531 335 588 838 961 206 956 608 670 924 [73] 361 236 722 897 734 927 485 817 701 550 492 524 909 566 400 950 385 500 [91] 176 192 576 951 634 801 813 137 889 221 747 354 974 973 315 444 317 569 [109] 408 878 950 475 418 187 300 570 380 730 415 328 490 274 289 674 576 440 [127] 473 565 864 552 303 232 242 115 611 732 880 460 981 288 198 494 137 995 [145] 736 493 555 920 948 686
示例
pdf_x4<-density(x4,from=111,to=999) pdf_x4输出结果
Call:
density.default(x = x4, from = 111, to = 999)
Data: x4 (150 obs.); Bandwidth 'bw' = 87.18
x y
Min. :111 Min. :0.0005505
1st Qu.:333 1st Qu.:0.0009550
Median :555 Median :0.0010272
Mean :555 Mean :0.0010283
3rd Qu.:777 3rd Qu.:0.0011339
Max. :999 Max. :0.0012438示例
x5<-sample(1:1000,50) x5输出结果
[1] 602 716 178 950 55 730 956 916 778 702 49 20 888 259 153 894 150 979 735 [20] 455 543 424 296 697 495 505 957 710 493 725 125 947 379 401 752 502 421 664 [39] 102 620 116 345 202 760 193 868 97 459 703 32
示例
pdf_x5<-density(x5,from=1,to=1000) pdf_x5输出结果
Call:
density.default(x = x5, from = 1, to = 1000)
Data: x5 (50 obs.); Bandwidth 'bw' = 123.9
x y
Min. : 1.0 Min. :0.0005498
1st Qu.: 250.8 1st Qu.:0.0008195
Median : 500.5 Median :0.0008665
Mean : 500.5 Mean :0.0008907
3rd Qu.: 750.2 3rd Qu.:0.0009993
Max. :1000.0 Max. :0.0010921