1概率函数

分布与R函数对应：

Screenshot_20220113_120852_tv.danmaku.bili_edit_39243700578985.jpg

Screenshot_20220113_121404_tv.danmaku.bili.png

在对应函数前加字母所表示：

• d：概率密度函数
• p：分布函数
• q：分布函数的反函数
• r：产生相同分布的随机数

描述性统计函数

summary函数

> summary(myvars)
      mpg              hp              wt              am        
 Min.   : 1.00   Min.   : 52.0   Min.   :1.513   Min.   :0.0000  
 1st Qu.: 8.75   1st Qu.: 96.5   1st Qu.:2.581   1st Qu.:0.0000  
 Median :16.50   Median :123.0   Median :3.325   Median :0.0000  
 Mean   :16.50   Mean   :146.7   Mean   :3.217   Mean   :0.4062  
 3rd Qu.:24.25   3rd Qu.:180.0   3rd Qu.:3.610   3rd Qu.:1.0000  
 Max.   :32.00   Max.   :335.0   Max.   :5.424   Max.   :1.0000  
#summary函数会得出该数据的一系列结果，包括最大最小值，四分位。。。

aggregate函数（分类分析）

> aggregate(iris[c("Sepal.Length","Sepal.Width")],by=list(iris$Species),max)
     Group.1 Sepal.Length Sepal.Width
1     setosa          5.8         4.4
2 versicolor          7.0         3.4
3  virginica          7.9         3.8
#（）内第一部分表示需要统计的量，第二部分表示分类的依据，第三部分为需要统计的方法

频数统计函数

有因子才能分组，分组之后才能进行频数统计

> head(mtcars)
                  mpg cyl disp  hp drat    wt  qsec vs am gear carb
Mazda RX4           1   6  160 110 3.90 2.620 16.46  0  1    4    4
Mazda RX4 Wag       2   6  160 110 3.90 2.875 17.02  0  1    4    4
Datsun 710          3   4  108  93 3.85 2.320 18.61  1  1    4    1
Hornet 4 Drive      4   6  258 110 3.08 3.215 19.44  1  0    3    1
Hornet Sportabout   5   8  360 175 3.15 3.440 17.02  0  0    3    2
Valiant             6   6  225 105 2.76 3.460 20.22  1  0    3    1
> mtcars$cyl <- as.factor(mtcars$cyl)#将所需要分组的列转换成因子
> split(mtcars,mtcars$cyl)#使用split函数将其分组
$`4`
                mpg cyl  disp  hp drat    wt  qsec vs am gear carb
Datsun 710     22.8   4 108.0  93 3.85 2.320 18.61  1  1    4    1
Merc 240D      24.4   4 146.7  62 3.69 3.190 20.00  1  0    4    2
Merc 230       22.8   4 140.8  95 3.92 3.150 22.90  1  0    4    2
Fiat 128       32.4   4  78.7  66 4.08 2.200 19.47  1  1    4    1
Honda Civic    30.4   4  75.7  52 4.93 1.615 18.52  1  1    4    2
Toyota Corolla 33.9   4  71.1  65 4.22 1.835 19.90  1  1    4    1
Toyota Corona  21.5   4 120.1  97 3.70 2.465 20.01  1  0    3    1
Fiat X1-9      27.3   4  79.0  66 4.08 1.935 18.90  1  1    4    1
Porsche 914-2  26.0   4 120.3  91 4.43 2.140 16.70  0  1    5    2
Lotus Europa   30.4   4  95.1 113 3.77 1.513 16.90  1  1    5    2
Volvo 142E     21.4   4 121.0 109 4.11 2.780 18.60  1  1    4    2

$`6`
                mpg cyl  disp  hp drat    wt  qsec vs am gear carb
Mazda RX4      21.0   6 160.0 110 3.90 2.620 16.46  0  1    4    4
Mazda RX4 Wag  21.0   6 160.0 110 3.90 2.875 17.02  0  1    4    4
Hornet 4 Drive 21.4   6 258.0 110 3.08 3.215 19.44  1  0    3    1
Valiant        18.1   6 225.0 105 2.76 3.460 20.22  1  0    3    1
Merc 280       19.2   6 167.6 123 3.92 3.440 18.30  1  0    4    4
Merc 280C      17.8   6 167.6 123 3.92 3.440 18.90  1  0    4    4
Ferrari Dino   19.7   6 145.0 175 3.62 2.770 15.50  0  1    5    6

$`8`
                     mpg cyl  disp  hp drat    wt  qsec vs am gear carb
Hornet Sportabout   18.7   8 360.0 175 3.15 3.440 17.02  0  0    3    2
Duster 360          14.3   8 360.0 245 3.21 3.570 15.84  0  0    3    4
Merc 450SE          16.4   8 275.8 180 3.07 4.070 17.40  0  0    3    3
Merc 450SL          17.3   8 275.8 180 3.07 3.730 17.60  0  0    3    3
Merc 450SLC         15.2   8 275.8 180 3.07 3.780 18.00  0  0    3    3
Cadillac Fleetwood  10.4   8 472.0 205 2.93 5.250 17.98  0  0    3    4
Lincoln Continental 10.4   8 460.0 215 3.00 5.424 17.82  0  0    3    4
Chrysler Imperial   14.7   8 440.0 230 3.23 5.345 17.42  0  0    3    4
Dodge Challenger    15.5   8 318.0 150 2.76 3.520 16.87  0  0    3    2
AMC Javelin         15.2   8 304.0 150 3.15 3.435 17.30  0  0    3    2
Camaro Z28          13.3   8 350.0 245 3.73 3.840 15.41  0  0    3    4
Pontiac Firebird    19.2   8 400.0 175 3.08 3.845 17.05  0  0    3    2
Ford Pantera L      15.8   8 351.0 264 4.22 3.170 14.50  0  1    5    4
Maserati Bora       15.0   8 301.0 335 3.54 3.570 14.60  0  1    5    8

对于因子不是很明显的数据进行分组前要先用cut函数进行分割

> cut(mtcars$mpg,c(seq(10,50,10)))#对目标列进行分割，从10分割到50，每10个分一组
 [1] (20,30] (20,30] (20,30] (20,30] (10,20] (10,20] (10,20] (20,30] (20,30]
[10] (10,20] (10,20] (10,20] (10,20] (10,20] (10,20] (10,20] (10,20] (30,40]
[19] (30,40] (30,40] (20,30] (10,20] (10,20] (10,20] (10,20] (20,30] (20,30]
[28] (30,40] (10,20] (10,20] (10,20] (20,30]
Levels: (10,20] (20,30] (30,40] (40,50]
> table(cut(mtcars$mpg,c(seq(10,50,10))))#使用table函数进行频数统计

(10,20] (20,30] (30,40] (40,50] 
     18      10       4       0 
> prop.table(table(cut(mtcars$mpg,c(seq(10,50,10)))))#使用prop.table函数对频数进行频率统计

(10,20] (20,30] (30,40] (40,50] 
 0.5625  0.3125  0.1250  0.0000 

对于二维数据（两列）的频数统计

> head(Arthritis)#载入数据集，该数据集里sex，treatment和improved都可以做因子，随便取两个进行统计
  ID Treatment  Sex Age Improved
1 57   Treated Male  27     Some
2 46   Treated Male  29     None
3 77   Treated Male  30     None
4 17   Treated Male  32   Marked
5 36   Treated Male  46   Marked
6 23   Treated Male  58   Marked
> table(Arthritis$Treatment,Arthritis$Improved)#选择treatment和improved作为统计，则返回一个表格，，前作为行，，后作为列表头为各自的level。
         
          None Some Marked
  Placebo   29    7      7
  Treated   13    7     21

#对于二维数据的频数统计还可以使用xtabs函数：
> xtabs(~Treatment+Improved,data=Arthritis)#~后跟想要统计的两个列名，data=数据集
         Improved
Treatment None Some Marked
  Placebo   29    7      7
  Treated   13    7     21
#使用prop.table函数进行频率统计，1为对行进行频率统计，2为列
> x <- xtabs(~Treatment+Improved,data=Arthritis)
> prop.table(x,1)
         Improved
Treatment      None      Some    Marked
  Placebo 0.6744186 0.1627907 0.1627907
  Treated 0.3170732 0.1707317 0.5121951

对于三维数据的频数统计

> y <- xtabs(~Treatment+Improved+Sex,data=Arthritis)#同二维数据一样使用xtabs函数
> ftable(y)#使用ftable函数使得结果更好看
                   Sex Female Male
Treatment Improved                
Placebo   None             19   10
          Some              7    0
          Marked            6    1
Treated   None              6    7
          Some              5    2
          Marked           16    5