#請記得先安裝TSA package 
library( TSA) 
 
#X~N(0,1) 
set.seed ( 1 ) 
par( mfrow= c( 1 , 2 ) ) 
popnorm<- rnorm( n= 100000 , mean= 0 ,  sd= 1 ) 
mean( popnorm) 
var( popnorm) 
plot( density( popnorm) ) 
meannorm<- array( 0 , dim= c( 1000 ) ) 
for  ( i in 1 : 1000 )  { 
meannorm[ i] = mean( sample( popnorm, size= 30 , replace= TRUE) ) 
} 
mean( meannorm) 
var( meannorm) 
plot( density( meannorm) ) 
jarque.bera .test ( meannorm) 
 
#X~U(-1,1) 
set.seed ( 1 ) 
par( mfrow= c( 1 , 2 ) ) 
popunif<- runif( n= 100000 , min=- 1 , max= 1 ) 
mean( popunif) 
var( popunif) 
plot( density( popunif) ) 
meanunif<- array( 0 , dim= c( 1000 ) ) 
for  ( i in 1 : 1000 )  { 
meanunif[ i] = mean( sample( popunif, size= 30 , replace= TRUE) ) 
} 
mean( meanunif) 
var( meanunif) 
plot( density( meanunif) ) 
jarque.bera .test ( meanunif) 
 
#X~Bin(1,0.1) 
set.seed ( 1 ) 
par( mfrow= c( 1 , 2 ) ) 
popbinom<- rbinom( n= 100000 ,  size= 1 ,  p= 0.1 ) 
mean( popbinom) 
var( popbinom) 
hist( popbinom) 
meanbinom<- array( 0 , dim= c( 1000 ) ) 
for  ( i in 1 : 1000 )  { 
meanbinom[ i] = mean( sample( popbinom, size= 30 , replace= TRUE) ) 
} 
mean( meanbinom) 
var( meanbinom) 
plot( density( meanbinom) ) 
jarque.bera .test ( meanbinom) 
 
#X~Poi(1) 
set.seed ( 1 ) 
par( mfrow= c( 1 , 2 ) ) 
poppois<- rpois( n= 100000 , lambda= 1 ) 
mean( poppois) 
var( poppois) 
hist( poppois) 
meanpois<- array( 0 , dim= c( 1000 ) ) 
for  ( i in 1 : 1000 )  { 
meanpois[ i] = mean( sample( poppois, size= 30 , replace= TRUE) ) 
} 
mean( meanpois) 
var( meanpois) 
plot( density( meanpois) ) 
jarque.bera .test ( meanpois) 
 
#X~Exp(1) 
set.seed ( 1 ) 
par( mfrow= c( 1 , 2 ) ) 
popexp<- rexp( n= 100000 , rate= 1 ) 
mean( popexp) 
var( popexp) 
plot( density( popexp) ) 
meanexp<- array( 0 , dim= c( 1000 ) ) 
for  ( i in 1 : 1000 )  { 
meanexp[ i] = mean( sample( popexp, size= 30 , replace= TRUE) ) 
} 
mean( meanexp) 
var( meanexp) 
plot( density( meanexp) ) 
jarque.bera .test ( meanexp) 
 
#X~Beta(0.1,5) 
set.seed ( 1 ) 
par( mfrow= c( 1 , 2 ) ) 
popbeta<- rbeta( n= 100000 , shape1= 0.1 ,  shape2= 5 ) 
mean( popbeta) 
var( popbeta) 
plot( density( popbeta) ) 
meanbeta<- array( 0 , dim= c( 1000 ) ) 
for  ( i in 1 : 1000 )  { 
meanbeta[ i] = mean( sample( popbeta, size= 30 , replace= TRUE) ) 
} 
mean( meanbeta) 
var( meanbeta) 
plot( density( meanbeta) ) 
jarque.bera .test ( meanbeta) 
 
#X~Cauchy(0,1) 
set.seed ( 1 ) 
par( mfrow= c( 1 , 2 ) ) 
popcauchy<- rcauchy( 100000 ,  location =  0 ,  scale =  1 ) 
mean( popcauchy) 
var( popcauchy) 
plot( density( popcauchy) ) 
meancauchy<- array( 0 , dim= c( 1000 ) ) 
for  ( i in 1 : 1000 )  { 
meancauchy[ i] = mean( sample( popcauchy, size= 30 , replace= TRUE) ) 
} 
mean( meancauchy) 
var( meancauchy) 
plot( density( meancauchy) ) 
jarque.bera .test ( meancauchy) 
 
 
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