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  今天,我們來分享一個(gè)統(tǒng)計(jì)學(xué)中非常重要的分布 ——
  正太分布 Normal distribution
  光聽名字就覺得極其可愛了 ....
  先來看看英文版的釋義:The normal distribution is a continuous probability distribution that, when graphed as a probability density, takes the form of the so-called bell-shaped curve.
  The bell shape results from the fact that, while the range of possible outcomes is infinite (negative infinity to positive infinity), most of the potential outcomes tend to be clustered relatively close to the distribution’s mean value.
  Just how close they are clustered is given by the standard deviation. In other words, a normal distribution is described completely by  two parameters: its mean (μ) and its standard deviation (σ).
  正態(tài)分布(Normal distribution)又名高斯分布(Gaussian distribution),因其曲線呈鐘形,因此人們又經(jīng)常稱之為鐘形曲線。
  正態(tài)曲線呈鐘型,兩頭低,中間高,左右對(duì)稱,曲線與橫軸間的面積總等于1。
  正態(tài)分布有兩個(gè)參數(shù),即均數(shù)μ和標(biāo)準(zhǔn)差σ,可記作N(μ,σ^2):均數(shù)μ決定正態(tài)曲線的中心位置;標(biāo)準(zhǔn)差σ決定正態(tài)曲線的陡峭或扁平程度。σ越小,曲線越陡峭;σ越大,曲線越扁平。
  u變換:為了便于描述和應(yīng)用,常將正態(tài)變量作數(shù)據(jù)轉(zhuǎn)換。μ是正態(tài)分布的位置參數(shù),描述正態(tài)分布的集中趨勢(shì)位置。正態(tài)分布以X=μ為對(duì)稱軸,左右完全對(duì)稱。正態(tài)分布的均數(shù)、中位數(shù)、眾數(shù)相同,均等于μ。
  σ描述正態(tài)分布資料數(shù)據(jù)分布的離散程度,σ越大,數(shù)據(jù)分布越分散,σ越小,數(shù)據(jù)分布越集中。也稱為是正態(tài)分布的形狀參數(shù),σ越大,曲線越扁平,反之,σ越小,曲線越瘦高。