#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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