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帕累托指數

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帕累托指數得名於意大利經濟學家和社會學家帕累托。在經濟學中,它測量了收入或財富分佈的寬度,是帕累托分佈的一個參數,反映了帕累托法則(20/80法則)。當應用於收入分佈時,帕累托法則有時被通俗地表述為:20%的人佔有80%的收入。事實上,帕累托在其《政治經濟學教程》一書中列舉的英國收入稅數據表明,大約20%的人口擁有大約80%的收入。

在用於收入分配模型時,對帕累托分佈的一種最簡單的表示是,收入x超過某一正數xm(x>xm)的人口比例為:

其中,xm是這一正數,即這一概率分佈的積分下界(m表示minimum)。帕累托指數就是參數α。由於人口比例必須介於0與1之間(包括0和1),參數α必須大於1。帕累托指數越大,極高收入人群的比例就越小。(當α=log(5)/log(4)≈1.16時,80/20定律嚴格成立;如果α=log(0.3)/log(3/7)≈1.42,則70/30定律成立。)

在數學上,上述公式要求所有收入至少達到正數的下界xm。在這一收入上,概率密度突然從0躍升,然後開始下降。這明顯是不符合現實的。因此,經濟學家有時認為帕累托法則只適用於收入分佈中表示較高收入的尾部。

另見

參考文獻

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