R Language Program

I believe a lot of the above I said the R language interested in it, share my information it. This is the R program for verifying the central limit theorem!

##### #验证: Regardless of which distribution the random variable was originally subjected to, as long as the sample size is large enough,

######## #其均数都会服从正态分布

# # #1. Normal Distribution # # #

A<-rnorm (10000,0,1) #生成一个数据量很大的正态分布的数据

x<-1:100 #生成一个向量用来存放样本均数的向量

A<-data.frame (a) #将这两个向量存放在数据框中

X<-data.frame (x)

Windows (1280,720);p ar (mfrow=c (2,2))

Plot (density (a$a), main = "This is the original distribution")

hist (A$a,main = "This is the original distribution")

For (i in 1:100) {#设置循环, loop over 100 samples and assign the calculated mean to the x variable in the data frame

C<-a[sample (Nrow (a), 1000),]

M=mean (c)

# print (m) #验证该循环可以正常工作

X$x[i]<-m

}

Plot (density (x$x), main = "This is the distribution of the mean of the sampled sample") #绘制抽取样本的均值的分布概率密度图

hist (A$a,main = "This is the distribution of the mean of the sampled sample")

# #将上面的程序加以改造 to verify other forms of distribution

# # # 2.0 Index Distribution # # # #

A<-rexp (100000,1) #生成一个数据量很大的指数分布的数据

x<-1:100 #生成一个用来存放样本均数的数据框

A<-data.frame (a) #将这两个向量存放在数据框中

X<-data.frame (x)

Windows (1280,720);p ar (mfrow=c)

Plot (density (a$a), main = "This is the original distribution")

For (i in 1:10000) {#设置循环, loop over 100 samples and assign the calculated mean to the x variable in the data frame

C<-a[sample (Nrow (a), 1000),]

M=mean (c)

# print (m) #验证该循环可以正常工作

X$x[i]<-m

}

Plot (density (x$x), main = "This is the distribution of the mean of the sampled sample") #绘制抽取样本的均值的分布概率密度图

# # # 3.0 T Distribution # # #

A<-rt (100,2) #生成一个数据量很大的t分布的数据

x<-1:1000 #生成一个用来存放样本均数的数据框

A<-data.frame (a) #将这两个向量存放在数据框中

X<-data.frame (x)

Windows (1280,720);p ar (mfrow=c)

Plot (density (a$a), main = "This is the original distribution") #查看原始数据的分布状态

For (i in 1:1000) {#设置循环, loop over 1000 samples and assign the calculated mean to the x variable in the data frame

C<-a[sample (Nrow (a), 10),]

M=mean (c)

# print (m) #验证该循环可以正常工作

X$x[i]<-m

}

Plot (density (x$x), main = "This is the distribution of the mean of the sampled sample") #绘制抽取样本的均值的分布概率密度图

# # #4.0 F Distribution # # # #

A<-RF (10000,1,5) #生成一个数据量很大的F分布的数据

x<-1:1000 #生成一个用来存放样本均数的数据框

A<-data.frame (a) #将这两个向量存放在数据框中

X<-data.frame (x)

Windows (1280,720);p ar (mfrow=c)

Plot (density (a$a), main = "This is the original distribution")

For (i in 1:1000) {#设置循环, loop over 1000 samples and assign the calculated mean to the x variable in the data frame

C<-a[sample (Nrow (a), 1000),]

M=mean (c)

# print (m) #验证该循环可以正常工作

X$x[i]<-m

}

Plot (density (x$x), main = "This is the distribution of the mean of the sampled sample") #绘制抽取样本的均值的分布概率密度图

# # #5.0 Chi Square Distribution # # # # #

A<-RCHISQ (100000,1) #生成一个数据量很大的卡方分布的数据

x<-1:1000 #生成一个用来存放样本均数的数据框

A<-data.frame (a) #将这两个向量存放在数据框中

X<-data.frame (x)

Windows (400,400);p ar (mfrow=c)

Plot (density (a$a), main = "This is a set of data that is presented in Chi-square distribution")

For (i in 1:1000) {#设置循环, loop over 100 samples and assign the calculated mean to the x variable in the data frame

C<-a[sample (Nrow (a), 1000),]

M=mean (c)

# print (m) #验证该循环可以正常工作

X$x[i]<-m

}

Plot (density (x$x), main = "This is the mean distribution of 1000 samples extracted from the data of the chi-square distribution")

#绘制抽取样本的均值的分布概率密度图

# # # 6.0 Function Solution # # # #

Myfun<-function (a) {

X<-1:100 #先生成一个1到100的序列, these values can be changed later, which is equivalent to overwriting the original value

X<-data.frame (x)

A<-data.frame (a)

For (i in 1:100) {#设置循环, loop over 100 samples and assign the calculated mean to the x variable in the data frame

C<-a[sample (Nrow (a), 1000),]

M=mean (c)

X$x[i]<-m

}

Windows (1280,720);p ar (mfrow=c (2,2))

Plot (density (a$a), main = "This is the original distribution")

hist (A$a,main = "This is the original distribution", col= ' Skyblue ')

Plot (density (x$x), main = "This is the distribution of the mean of the sampled sample")

hist (A$a,main = "This is the distribution of the mean of the sampled sample", Col= ' Skyblue ')

}

# # #6.1 Normal Distribution # # #

A<-rnorm (10000,0,1)

Myfun (a)

# # #6.2 Index Distribution # # # # #

B<-rexp (100000,1)

Myfun (b)

# # #6.3 T Distribution # # # #

C<-rt (1000,3)

Myfun (c)

# # #6.4 F Distribution # # # #

D<-RCHISQ (100000,1)

Myfun (d)

R Language Program