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1、书山有路 期末考试专项复习 一 矩阵与数据框 1 生成特定的矩阵与数据框 矩阵 方法一a array 1 10 dim c 2 5 rownames a 1 2colnames a c one two three four five adimnames a list 1 2 c one two three four five nrow nrow a ncol ncol a dim a 方法二a matrix 1 10 nrow 2 byrow F rownames a 1 2colnames a c one two three four five a matrix 1 10 nrow 2 by
2、row F dimnames list 1 2 c one two three four five 数据框的生成df data frame Name c Alice Becka James Jeffrey John Sex c F F M M M Age c 13 13 12 13 12 Height c 56 5 65 3 57 3 62 5 59 0 Weight c 84 0 98 0 83 0 84 0 99 5 dfLst list Name c Alice Becka James Jeffrey John Sex c F F M M M Age c 13 13 12 13 12 H
3、eight c 56 5 65 3 57 3 62 5 59 0 Weight c 84 0 98 0 83 0 84 0 99 5 LstLst Name Lst Name Lst 1 Lst 1 Lst Name 1 书山有路df as data frame Lst dfx array 1 6 dim c 2 3 as data frame x 数据框的引用df 1 2 3 5 df Height df Weightnames df 此属性一定非空rownames df c one two three four five dfattach df r Height Weightrdf r r
4、names df detach r Height Weight 2 矩阵的运算a diag 1 3 a 2 1 1a 1转置运算t a 2行列式det a 3向量内积x 1 5y 2 1 5x yt x ycrossprod x y 4向量的外积x t y tcrossprod x y outer x y x o y 矩阵的乘法a array 1 9 dim c 3 3 b array 9 1 dim c 3 3 x 1 3a ba bx a x 2 书山有路crossprod a b t a btcrossprod a b a t b 矩阵的逆solve a b 1 3solve a b a
5、x b的解 矩阵的特征值与特征向量sm eigen a sme diag 1 3 svde svd e svdeattach svde u diag d t v 与矩阵运算有关的函数 取维数a diag 1 4 nrow a ncol a 矩阵的合并x1 rbind c 1 2 c 3 4 x2 x1 10 x3 cbind x1 x2 x3x4 rbind x1 x2 x4cbind 1 x1 矩阵的拉直a matrix 1 6 ncol 2 dimnames list c one two three c first second byrow T as vector a apply函数app
6、ly a 1 mean apply a 2 sum tapply 1 5 factor c f f m m m mean 第二题 产生随机数x rnorm 100 0 1 x 画随机数的直方图hist x freq F 核密度曲线density x 3 书山有路lines density x col blue 添加正态分布分布函数y seq 4 3 0 2 lines y dnorm y mean x sd x col red 画随机数的经验分布函数z rnorm 50 0 1 plot ecdf z do p F verticals T d seq 3 2 0 2 lines d pnorm
7、 d mean z sd z col red y rpois 100 2 plot ecdf y col red verticals T do p F x 0 8lines x ppois x mean y col blue w c 75 64 47 4 66 9 62 2 62 2 58 7 63 5 66 6 64 0 57 0 69 0 56 9 50 0 72 0 hist w freq F lines density w col blue x 44 76lines x dnorm x mean w sd w col red plot ecdf w do p F verticals T
8、 lines x pnorm x mean w sd w col red 编写函数求随机数的各种描述统计量data outline function x n length x m mean x v var x s sd x me median x cv 100 s mcss sum x m 2 uss sum x 2 R max x min x 样本极差R1 quantile x 3 4 quantile x 1 4 四分位差sm s sqrt n 样本标准误g1 n n 1 n 2 sum x m 3 s 3g2 n n 1 n 1 n 2 n 3 sum x m 4 s 4 3 n 1 2
9、 n 2 n 3 data frame N n Mean m Var v std dev s Median me std mean sm CV cv CSS css USS uss R R R1 R1 Skewness g1 Kurtosis g2 row names 1 x rnorm 100 data outline x 4 书山有路 第三题 r p q drnorm 100 0 1 pnorm 1 5 0 1 dnorm 3 3 0 1 qnorm seq 0 1 0 25 0 1 rbeta 100 2 2 rbinom 100 100 0 5 pbinom 1 100 100 0 5
10、 dbinom 1 5 100 0 5 qbinom seq 0 1 0 1 100 0 5 rchisq 100 1 qchisq seq 0 1 0 2 10 pchisq 1 10 10 dchisq 1 10 10 rexp 100 0 5 rpois 100 2 ppois 1 1000 2 dpois 1 100 2 runif 100 0 1 qunif c 0 0 2 0 8 0 1 punif seq 0 1 0 2 0 1 dunif seq 0 1 0 01 0 1 rt 100 2 qt 0 8 2 pt 3 3 2 dt 3 3 2 rf 100 1 2 qf 0 8
11、 1 2 四置信区间 1 1 sigma已知interval estimate1 function x side 0 sigma 1 alpha 0 05 xb mean x n length x if side0 tmp sigma sqrt n qnorm 1 alpha a xb tmp b Inf else 5 书山有路tmp sigma sqrt n qnorm 1 alpha 2 a xb tmp b xb tmp data frame mean xb a a b b x rnorm 100 0 4 interval estimate1 x sigma 4 side 0 inter
12、val estimate1 x sigma 4 side 1 interval estimate1 x sigma 4 side 1 2 sigma未知interval estimate2 function x side 0 alpha 0 05 xb mean x n length x if side0 tmp sd x sqrt n qt 1 alpha n 1 a xb tmp b Inf else tmp sd x sqrt n qt 1 alpha 2 n 1 a xb tmp b xb tmp data frame mean xb a a b b x rnorm 100 0 1 i
13、nterval estimate2 x side 1 interval estimate2 x side 0 interval estimate2 x side 1 t test x side 1 t test x side 0 t test x side 1 两个总体sigma1 sigma2但未知interval estimate3 function x y alpha 0 05 xb mean x yb mean y n1 length x n2 length y sw n1 1 var x n2 1 var y n1 n1 2 tmp sqrt 1 n1 1 n2 sw qt 1 al
14、pha 2 n1 n2 2 a xb yb tmp b xb yb tmpdata frame mean xb yb a a b b x rnorm 100 0 1 y rnorm 100 1 1 interval estimate3 x y 6 书山有路t test x y 0 03643479 0 98699097 第五题假设检验 1 sigam已知 双侧 检验mu mu0mean test1 function x mu 0 sigma 1 xb mean x n length x z xb mu sigma sqrt n p pnorm z if p 1 2 P 2 pelseP 2 1
15、 p data frame mean xb Z z p value P x rnorm 100 0 2 mean test1 x mu 0 sigma 2 2 sigma未知 双侧 检验mu mu0mean test2 function x mu 0 xb mean x n length x z xb mu sd x sqrt n p pt z n 1 if p 1 2 P 2 pelseP 2 1 p data frame mean xb Z z p value P x rnorm 100 mean test2 x mu 0 t test x mu 0 alt two side 两个总体si
16、gma1 sigma2但未知 检验mu1 mu2mean test3 function x y mu 0 xb mean x yb mean y n1 length x n2 length y sw n1 1 var x n2 1 var y n1 n2 2 t xb yb mu sqrt sw 1 n1 1 n2 p pt t n1 n2 1 if p 1 2 P 2 pelseP 2 1 p data frame mean xb yb T t p value P x rnorm 100 0 1 7 书山有路y rnorm 100 2 1 mean test3 x y mu 2 t test x y var equal T mu 2 x rnorm 100 0 1 y rnorm 100 0 2 mean test3 x y t test x y var equal T 第六题调用R函数 k s检验两组数是否同分布x rnorm 100 0 1 y rt 100 5 z rnorm 100 0 1 ks test x y alt l ks test x z 检验一组数是否服从已知分布
