Sampling Distribution

今天被人問到『那你覺得sampling distribution為什麼可以求出來？』
一時之間還真不知道該怎樣解釋..很擔心自己學的和他學的名詞會有落差
用google查一下..

原文來自於Wikipeida Sampling distribution
中文是我自己翻譯的，看的懂就好..我沒有太花心思去翻譯

In statistics, a sampling distribution is the probability distribution, under repeated sampling of the population, of a given statistic (a numerical quantity calculated from the data values in a sample).
統計上樣本分配一種機率分配，根據從母體產生的試驗(樣本)中產生之統計量的分配

The formula for the sampling distribution depends on the distribution of the population, the statistic being considered, and the sample size used. A more precise formulation would speak of the distribution of the statistic as that for all possible samples of a given size, not just "under repeated sampling".
樣本分配的公式主要受到以下幾點因素影響：母體分配、使用的統計量、以及使用的樣本數
可以更精準的說是『固定樣本數下所有可能樣本得到的統計量分配』而非單純重複的抽樣而已

For example, consider a very large normal population (one that follows the so-called bell curve). Assume we repeatedly take samples of a given size from the population and calculate the sample mean (\bar x, the arithmetic mean of the data values) for each sample. Different samples will lead to different sample means. The distribution of these means is the "sampling distribution of the sample mean" (for the given sample size). This distribution will be normal since the population was normal. (According to the central limit theorem, if the population is not normal but "sufficiently well behaved", the sampling distribution of the sample mean will still be approximately normal provided the sample size is sufficiently large.)
例如：假設一個很大的常態分配。假設重複的得到固定size的樣本
並且計算樣本的平均值已計算統計量，因為重複試驗造成每次得到的樣本平均值會有所差異
這些樣本平均值的分配就是樣本分配。
該分配是常態分配，因為母體是常態，甚至於如果母體非常態分配，只要樣本量夠大，根據中央極限定理，也會得到常態分配的值。

後話：
自己一開始就把人家要做的東西推翻是一種很不好的習慣，要改進！就算母體是一個參數，樣本還是可以推導出分配，不過到底意義在哪裡..我覺得是可以好好思考的地方～～