Membuat Distribusi Normal Acak Menggunakan rnorm()

set.seed(300) # Setting the seed for replication purposes
myData <- rnorm(2000,20,4.5) # Creating a random normal distribution (n=300, mean=20, sd=4.5)

Melakukan Pemeriksaan Awal (Sanity Checks) pada myData Menggunakan length(), mean(), dan sd()

length(myData) # How many observations?

## [1] 2000

mean(myData) # What is the mean?

## [1] 20.25773

sd(myData) # What is the standard deviation?

## [1] 4.590852

Membuat Grafik untuk myData

# Membuat histogram dari myData
hist(myData, breaks = 30, col = "lightblue", main = "Distribusi myData", xlab = "Nilai", ylab
= "Frekuensi")

# Menambahkan garis vertikal untuk mean
abline(v = mean(myData), col = "red", lwd = 2, lty = 2)
# Menambahkan legenda

legend("topright", legend = paste("Mean =", round(mean(myData), 5)), col = "red", lty = 2, lwd = 2)

Resampling dari myData Sebanyak 1000 Kali Menggunakan for(iin x)

set.seed(200) # Setting the seed for replication purposes

sample.size <- 2000 # Sample size

n.samples <- 1000 # Number of bootstrap samples

bootstrap.results <- c() # Creating an empty vector to hold the results

for (i in 1:n.samples)
{
obs <- sample(1:sample.size, replace=TRUE)
bootstrap.results[i] <- mean(myData[obs]) # Mean of the bootstrap sample
}

length(bootstrap.results) # Sanity check: this should contain the mean of 1000 different samples

## [1] 1000

summary(bootstrap.results) # Sanity check

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   19.92   20.19   20.26   20.26   20.33   20.57

sd(bootstrap.results) # Checking the standard deviation of the distribution of means (this is what we are interested in!)

## [1] 0.1021229

par(mfrow=c(2,1), pin=c(5.8,0.98)) # Combining plots (2 rows, 1 column) and setting the plots size

hist(bootstrap.results, # Creating an histogram
    col="red", # Changing the color
    xlab="Mean", # Giving a label to the x axis
    main=paste("Means of 1000 bootstrap samples from myData")) # Giving a title to the graph

hist(myData, # Creating an histogram
    col="magenta", # Changing the color
    xlab="Value", # Giving a label to the x axis
    main=paste("Distribution of myData")) # Giving a title to the graph

Pengambilan sampel ulang sebanyak 1000 kali dari proses pembuatan data aktual menggunakan for(i in x)

set.seed(200) # Setting the seed for replication purposes

sample.size <- 2000 # Sample size

n.samples <- 1000 # Number of bootstrap samples

bootstrap.results <- c() # Creating an empty vector to hold the results
for (i in 1:n.samples)
{
bootstrap.results[i] <- mean(rnorm(2000,20,4.5)) # Mean of the bootstrap sample
}

length(bootstrap.results) # Sanity check: this should contain the mean of 1000 different samples

## [1] 1000

summary(bootstrap.results) # Sanity check

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   19.64   19.93   20.00   20.00   20.07   20.32

sd(bootstrap.results) # Checking the standard deviation of the distribution of means (this is what we are interested in!)

## [1] 0.1041927

par(mfrow=c(2,1), pin=c(5.8,0.98)) # Combining plots (2 rows, 1 column) and setting the plots size

hist(bootstrap.results, # Creating an histogram
    col="#d83737", # Changing the color
    xlab="Mean", # Giving a label to the x axis
    main=paste("Means of 1000 bootstrap samples from the DGP")) # Giving a title to the graph

hist(myData, # Creating an histogram
    col="#37aad8", # Changing the color
    xlab="Value", # Giving a label to the x axis
    main=paste("Distribution of myData")) # Giving a title to the graph

Exercises

Latihan 1

Tetapkan benih Anda pada angka 150. Hasilkan distribusi normal acak dari 1000 observasi, dengan rata-rata 30 dan simpangan baku 2,5. Hitung rata-rata dari 50 sampel dari 1000 observasi dari kumpulan data tersebut. Simpan hasil Anda dalam vektor.

Fungsi yang relevan: set.seed(), rnorm(), for(i in x), sample().

Answer:

set.seed(150)

data <- rnorm(1000, mean = 30, sd = 2.5)

sample_means <- c()

for (i in 1:50) {
  sample_i <- sample(data, size = 50, replace = FALSE)
  sample_means[i] <- mean(sample_i)
}

sample_means

##  [1] 29.88923 29.12852 29.96403 30.28330 29.42555 30.13464 29.83227 29.61958
##  [9] 30.36293 29.70179 30.39229 29.90397 29.45825 29.69616 30.47237 29.73355
## [17] 29.83181 30.24189 30.10936 30.43929 29.87055 30.00566 29.53994 30.10614
## [25] 30.37129 29.70682 29.74007 30.11853 29.86817 30.03286 30.09281 30.18419
## [33] 29.60297 29.83622 30.02769 30.69890 29.68912 29.64516 29.05322 29.63437
## [41] 30.41860 29.68675 29.47005 29.46992 29.60059 29.92465 29.71743 29.91258
## [49] 29.72997 30.05085

Latihan 2

Hasilkan dua histogram untuk menampilkan secara grafis distribusi rata-rata yang diperoleh dalam Latihan 1 serta nilai dari 1000 observasi dalam kumpulan data asli Anda. Gabungkan histogram ini menjadi satu grafik keseluruhan.

Fungsi yang relevan: par(), hist().