用Python學(xué)線性代數(shù)：自動(dòng)擬合數(shù)據(jù)分布

問題

如果有一組數(shù)據(jù)，如何確定他們來自哪個(gè)統(tǒng)計(jì)分布？

從數(shù)據(jù)分析的角度，我們并不想要通過嚴(yán)格的統(tǒng)計(jì)方法去找到這個(gè)分布，其實(shí) Python 中有一個(gè)可以自動(dòng)擬合數(shù)據(jù)分布的庫(kù) —— distfit ?。這是一個(gè)python包，用于通過殘差平方和（RSS）和擬合優(yōu)度檢驗(yàn)（GOF）對(duì)89個(gè)單變量分布進(jìn)行概率密度擬合，并返回最佳分布。

distfit 簡(jiǎn)單又好用

#?安裝
pip?install?distfit

常見用法：

.fit_transform(): 在經(jīng)驗(yàn)數(shù)據(jù) X 上擬合分布
.summary:獲得擬合數(shù)據(jù)并測(cè)試擬合優(yōu)度的所有分布的分?jǐn)?shù)。
.predict():預(yù)測(cè)響應(yīng)變量的概率
.model：輸出分布的最佳參數(shù)
.plot(): 繪制最佳的擬合分布

示例

from?distfit?import?distfit
import?numpy?as?np
X?=?np.random.normal(0,?2,?[100,10])
y?=?[-8,-6,0,1,2,3,4,5,6]
dist?=?distfit(todf=True)
dist.fit_transform(X)
dist.plot()

輸出用于擬合過程的函數(shù)列表，它使用最流行的 10 個(gè)發(fā)行版的列表進(jìn)行掃描。

[distfit]?>[norm??????]?[0.00?sec]?[RSS:?0.0120713]?[loc=-0.047?scale=1.984]
[distfit]?>[expon?????]?[0.0?sec]?[RSS:?0.4092169]?[loc=-7.320?scale=7.273]
[distfit]?>[pareto????]?[0.06?sec]?[RSS:?0.4098607]?[loc=-98251992.546?scale=98251985.226]
[distfit]?>[dweibull??]?[0.01?sec]?[RSS:?0.0229391]?[loc=-0.046?scale=1.721]
[distfit]?>[t?????????]?[0.04?sec]?[RSS:?0.0120717]?[loc=-0.047?scale=1.984]
[distfit]?>[genextreme]?[0.05?sec]?[RSS:?0.0107445]?[loc=-0.755?scale=1.981]
[distfit]?>[gamma?????]?[0.04?sec]?[RSS:?0.0118907]?[loc=-191.812?scale=0.021]
[distfit]?>[lognorm???]?[0.09?sec]?[RSS:?0.0117103]?[loc=-107.148?scale=107.084]
[distfit]?>[beta??????]?[0.03?sec]?[RSS:?0.0116300]?[loc=-14.479?scale=28.973]
[distfit]?>[uniform???]?[0.0?sec]?[RSS:?0.2545746]?[loc=-7.320?scale=12.835]
[distfit]?>[loggamma??]?[0.04?sec]?[RSS:?0.0123738]?[loc=-360.941?scale=54.518]

當(dāng)然，distfit 支持的分布還有很多：

最后繪制最佳的擬合分布

dist.summary 輸出各分布的參數(shù)。

?????????distr??????score??...???????scale???????????????????????????????????????arg
0???genextreme??0.0107445??...??????1.9814????????????????????(0.27387377680364405,)
1?????????beta????0.01163??...?????28.9726??(26.055079164665887,?26.248878389403494)
2??????lognorm??0.0117103??...?????107.084????????????????????(0.01848064379707136,)
3????????gamma??0.0118907??...???0.0205321??????????????????????(9339.777394183824,)
4?????????norm??0.0120713??...?????1.98429????????????????????????????????????????()
5????????????t??0.0120717??...?????1.98428??????????????????????(1863131.339823592,)
6?????loggamma??0.0123738??...?????54.5178??????????????????????(750.2645425001494,)
7?????dweibull??0.0229391??...?????1.72129?????????????????????(1.2898970802235787,)
8??????uniform???0.254575??...?????12.8346????????????????????????????????????????()
9????????expon???0.409217??...?????7.27316????????????????????????????????????????()
10??????pareto???0.409861??...??9.8252e+07?????????????????????(13542571.060345018,)