平均數及變異數的抽樣分配(Distribution of Mean and Variance)

為什麼這些估計值會是隨機變數呢?

Julia程式碼

using Random, Distributions, Plots; pyplot()

Random.seed!(0)

# 假設母體分配為exponetial distribution

lambda  = 1/4.5

expDist = Exponential(1/lambda)

# n為每一次抽樣的樣本大小

# N為抽樣次數

n, N    = 10, 10^6

means     = Array{Float64}(undef, N)

variances = Array{Float64}(undef, N)

# 開始進行模擬抽樣，重複N次

for i in 1:N

    # 隨機(模擬)抽取樣本資料

    data = rand(expDist,n)

    # 計算樣本平均及變異數

    means[i] = mean(data)

    variances[i] = var(data)

end

# 理論的平均和抽樣得出的樣本平均

println("Actual mean: ",mean(expDist),

        "\nMean of sample means: ",mean(means))

println("Actual variance: ",var(expDist),

    "\nMean of sample variances: ",mean(variances))

# 用直方圖表示其分配

stephist(means, bins=200, c=:blue, normed=true,

    label="Histogram of Sample Means")

stephist!(variances, bins=600, c=:red, normed=true,

    label="Histogram of Sample Variances", xlims=(0,40), ylims=(0,0.4),

        xlabel = "Statistic value", ylabel = "Density")

Originally published at on August 6, 2020.