為什麼這篇高斯分布鄉民發文收入到精華區：因為在高斯分布這個討論話題中，有許多相關的文章在討論，這篇最有參考價值！作者sld (天佑台灣)看板Statistics標題Re: [問題] 常態(高斯)分布的推導時間Tu...
高斯分布 在 辣媽英文天后 林俐 Carol Instagram 的最讚貼文
2021-07-06 05:58:15
哇！英數合鳴！ 這週四晚上7:30～8:30 —> 李傑老師 @jackleemath 這週六晚上7:30～8:30 —> 俐媽 我們即將要舉辦國三升高一線上直播活動了， 內容精彩、抽獎獎項豐富， 歡迎大家來喔！ 今天，送上北一學姊編整的「數學篇」，剛好是英+數合體的最佳表現！ ——————...
: 推 zevin:你可視它為定義，定義pdf長那樣的機率分配為常態分配 10/10 17:31
: → zevin:或者你應該問，為什麼要把pdf長那樣的機率分配叫做常態分配 10/10 17:36
: 推 daa94:但是老師要我推導公式證明Orz....我已經弄一整天了 嗚 10/10 17:43
: 推 zevin:但是你給的這個網頁，下面也有寫說這是常態分布的定義..... 10/10 17:53
: 推 zevin:我學了很久的統計跟機率，也沒聽過常態pdf的證明 10/10 17:57
: → zevin:一般而言都是視為定義吧 10/10 17:58
應該不是定義喔.
很多 distribution 都是依據一些性質而推導出來的,
不是可以愛定成怎樣就怎樣.
比如有名的 Poisson distribution 也是根據一些假設的性質而推導出來的.
給原 po, 我不知道到底怎麼導出來的.
但是我看了一下 wiki, 裡面提到最初的文章是跟中央極限定理有關.
(我猜大概是 Binomial 在 n 很大時收斂到的 distribution 稱為 normal,
諸如此類的)
聽說學長們以前上機率課印象中老師有推導過,
似乎是從 wiki 裡提到從重複的 experiments然後看 errors,
設了一些假設然後可以推導出 normal 的 pdf.
不過真的不記得了.
你可以從這幾個方向去查查看有沒有幫助.
Google 一下這些前輩的文章等等.
我順便附上 wiki 的解釋
History
The normal distribution was first introduced by Abraham de Moivre in an
article in 1734 (reprinted in the second edition of his The Doctrine of
Chances, 1738) in the context of approximating certain binomial distributions
for large n. His result was extended by Laplace in his book Analytical Theory
of Probabilities (1812), and is now called the theorem of de Moivre-Laplace.
Laplace used the normal distribution in the analysis of errors of
experiments. The important method of least squares was introduced by Legendre
in 1805. Gauss, who claimed to have used the method since 1794, justified it
rigorously in 1809 by assuming a normal distribution of the errors.
The name "bell curve" goes back to Jouffret who first used the term "bell
surface" in 1872 for a bivariate normal with independent components. The name
"normal distribution" was coined independently by Charles S. Peirce, Francis
Galton and Wilhelm Lexis around 1875. This terminology is unfortunate, since
it reflects and encourages the fallacy that many or all probability
distributions are "normal". (See the discussion of "occurrence" below.)
That the distribution is called the Gaussian distribution is an instance of
Stigler's law of eponymy: "No scientific discovery is named after its
original discoverer."
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※ 編輯: sld 來自: 140.109.74.145 (10/10 18:16)