[定稿]非参数统计王星版第一章课后答案

非参数统计王星版第一章课后答案
非参数统计第一章课后答案
#1.1
AGE=c(18,23,22,21,20,19,20,20,20)
first3=sort(AGE)[(length(AGE)-2):length(AGE)] delete.1=order(AGE)[(length(AGE)-2):length(AGE)] except=AGE[-delete.1]
c(except[1:2],19,except[3:length(except)]) except[2]=22
#1.2
a1=rep(1:3,rep(2,3))
a2=c(1,8,10,11)
a3=seq(1,30,length(a2))
a4=seq(1,5,2)
a4=c(a1,a4,rep(0,2))
a5=2:10
a6=c(a2,a3[-(1:3)],a4)
a7=c(rep(1,10),rep(0,8))
#1.3
library(MASS)
data(geyser)
a=geyser
a1=subset(a,waiting<70)
a1=geyser[geyser$waiting<70,]#两个a1等价
a2=subset(a,waiting<70&waiting!=57)
a2=geyser[geyser$waiting<70&geyser$waiting!=57,]#两个a2等价
a3=subset(a,waiting<70,c(duration))
a4=subset(a,duration>70,c(waiting))
#1.3
library(MASS)
a=geyser
attach(a)
b1=waiting[waiting<70]
b2=waiting[waiting<70&waiting!=57]
b3=duration[waiting<70]
b4=waiting[duration>70]
#1.4
x=c(0,1,1,2,3,4)
num=function(x){
r=0
p=c(rep(0,length(x)-1))
q=c(rep(0,length(x)-1))
for(i in 1:(length(x)-1))
{
for(j in (i+1):length(x)){
p[i]=p[i]+I(x[i]<x[j])
q[i]=q[i]+I(x[i]>x[j])
}
r=r+p[i]-q[i]
}
r
}
h=rep(0,1000)
x=runif(5,-5,5)
h[i]=num(x)
}
y=as.factor(h)
yy=levels(y)
a=rep(0,11)#记数记录-10:10:2各种结果出现的次数
p=rep(0,11)
for(i in 1:11){
a[i]=sum(h==(-12+2*i))
p[i]=a[i]/length(h)
}
a
p
hist(h)
h=rep(0,10000)
for(i in 1:length(h)){
x=sample(1:5,5,replace=T)#-5到5中间的整数随机抽样
h[i]=num(x)
}
y=as.factor(h)
yy=levels(y)
a=rep(0,length(yy))#记数记录-10:10各种结果出现的次数p=rep(0,length(yy))
a[i]=sum(h==(-11+i))
p[i]=a[i]/length(h)
}
a
p
hist(h)
#当随机取10000次的一个结果 a=[71 321 774 1255 1637 1825 1684 1256 743 338 96]
# p=[0.0071 0.0321 0.0774 0.1255 0.1637 0.1825 0.1684 0.1256 0.0743 0.0338 0.0096]
#当随机取十万次数据的一个结果
#a=[795 3421 7553 12521 16771 18180 16538 12553 7418 3400 850]
#p=[0.00795 0.03421 0.07553 0.12521 0.16771 0.18180 0.16538 0.12553 0.07418 0.03400 0.00850]
#1.5
uniroot(f=function(x) 2*x^3-4*x^2+3*x-6, interval=c(-10,10))
f=function(x){2*x^3-4*x^2+3*x-6}
f(0)
a=-10
b=10
root=function(a,b)
{
c=(a+b)/2;
while(abs(f(c))>0.00001){
if(f(c)*f(a)<0){b=c; c=(a+b)/2;}
else {a=c; c=(a+b)/2;}}
c
#1.6
x=seq(0,2*pi,0.2)
y=sin(x)/(cos(x)+x)
#1.7
chartonum=function(x){
a=c("abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ");
b=strsplit(a,"");
for(i in 1:52){
if(b[[1]][i]==x){t=i;i=i+1}
else{i=i+1}
}
t
}#将字符转化为数字，小写为前26位，大写为后26位，输入为单个字符
f7=function(x){
y=strsplit(x,"");#将输入分为单个字符
for(i in 1:length(y[[1]])){
t=chartonum(y[[1]][i])
if(t<14){t=t+13;y[[1]][i]=LETTERS[t];}
else if(t>=14&t<=26){t=t-13;y[[1]][i]=LETTERS[t];}
else if(t>=27&t<=39){t=t+13-26;y[[1]][i]=letters[t];}
else{t=t-13-26;y[[1]][i]=letters[t];} }
mima=y;
mima
}
#1.8
f1.81=function(a){
for(i in 1:length(a))
{c[i]=a[length(a)-i+1]}
c
}
f1.82=function(a,b){
for(i in 1:(length(a)+length(b))){
if(i%%2==1){c[i]=a[(i+1)/2];}
else{c[i]=b[i/2];}
}
c
}#%%为求余符号
#1.9
f1.9=function(n,m){
a=rep(1,n);
i=1;
k=0;
t=1;
while(sum(a)>1|a[t]==0){
t=i%%n;
if(t==0){t=n;}
else{t=i%%n}
if(a[t]!=0){
k=k+1;i=i+1;}
else{i=i+1}
if(k%%m==0){k=0;a[t]=0;}
}
t
}
#1.10
student<-read.table("C:\\Documents and
Settings\\Administrator\\桌面\\非参数统计配套数据\\各章数据\\第一章\\student.txt",header
= T)
student1=as.data.frame(student)
means=apply(student1[,2:6],1,mean)
b1=data.frame(student1,means)
b2=student1[which(b==max(b)),]
b3=I(student1[,2:6]<60)#判断每个学生每门课程是否及格
b4=apply(b3,1,sum)#找出每个学生有几门课程不及格
b5=b1[which(b4>1),]
b6=b1[-which(b4>1),]
t.test(b5$means,b6$means)
#不说明情况下认为两总体方差不同，特殊说明var.equal=TRUE 置信区间为均值差的置信区间
wilcox.test(b5$means,b6$means)
wilcox.test(b5$means,b6$means,paires=FALSE)
#1.11
basket<-read.table("C:\\Documents and
Settings\\Administrator\\桌面\\非参数统计配套数据\\各章数据\\第一章\\basket.txt",header
= T)
A=I(basket[,2:6]=='A')
A=basket[,2:6]=='A'
Asum=apply(A,1,sum)
B=basket[,2:6]=='B'
Bsum=apply(B,1,sum)
a1=basket[which(Asum>0&Bsum>0),1]
length(a1)#求个数
a2=basket[which(Asum>0&Bsum>=3),]
length(a2$ID)#求个数
#1.12
x=seq(-10,10,0.05)
y1=sin(x)
y2=cos(x)
y3=y1+y2
plot(x,y1,col=1,lty=1,axes=T,main="习题1.12",sub="sin（）,cos （）,sin()+cos()对比图")
points(x,y2,col=2,lty=3)
points(x,y3,col=3,lty=4)
plot(x,y1,col=1,lty=1,main="习题1.12",sub="sin（）,cos （）,sin()+cos()对比图")
lines(x,y1,col=1,lty=1)
lines(x,y2,col=2,lty=3)
lines(x,y3,col=3,lty=4)
curve(sin(x),-10,10,col=1,lty=1,main="习题1.12",sub="sin （）,cos（）,sin()+cos()对比图")
curve(cos(x),add=TRUE,col=2,lty=3)
curve(sin(x)+cos(x),add=TRUE,col=3,lty=4)
#1.13
x=seq(-5,5,length=50)
a=runif(500,-5,5)
y=0.1*a*sin(2*a)
f1=function(x,y){1-exp(-1/x^2+y^2)}
z1=outer(x/2,x/2,f1)
persp(z1)
f2=function(x,y){0.1*x*sin(2*y)}
z2=outer(x,x,f2)
persp(z2)
f3=function(x,y){sin(x)+cos(x)}
z3=outer(x,x,f3)
persp(z3)
plot(sin(3*x),sin(6*x),type="l")
#1.14
a=rnorm(100,3,sqrt(5))
b=rnorm(20,5,sqrt(3))
c=c(a,b)
hist(c)
boxplot(c)
qqnorm(c)
#1.15
x=rnorm(100,0,1)
y1=log(abs(x))#lamda=0 hist(y1)
qqnorm(y1)
qqline(y1, col = 2)
y2=(x-1)#lamda=1
hist(y2)
qqnorm(y2)
qqline(y2, col = 3)
y3=1-1/x#lamda=-1
hist(y3)
qqnorm(y3)
qqline(y2, col = 4)。