我们定义了多元伽马分布${<trans\; data-src="R">R（右）</trans>}^{\mathrm{<trans\; data-src="n">n个</trans>}}$通过拉普拉斯变换${<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="P">P（P）</trans>}<trans\; data-src="(">(</trans><trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans><trans\; data-src=")">)</trans>}^{<trans\; data-src="-">-</trans>\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}}$，$\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}\mathrm{<trans\; data-src=">">></trans>}\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">，</trans>$哪里

$\mathrm{<trans\; data-src="P">P（P）</trans>}<trans\; data-src="(">(</trans>\mathrm{<trans\; data-src="\theta ">\theta </trans>}<trans\; data-src=")">)</trans><trans\; data-src="=">=</trans>{<trans\; data-src="\sum ">\sum </trans>}_{\mathrm{<trans\; data-src="T">T型</trans>}<trans\; data-src="\subset ">\subset </trans><trans\; data-src="\{">\{</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=",">，</trans><trans\; data-src="\dots ">\dots </trans><trans\; data-src=",">，</trans>\mathrm{<trans\; data-src="n">n个</trans>}<trans\; data-src="\}">\}</trans>}{\mathrm{<trans\; data-src="p">第页</trans>}}_{\mathrm{<trans\; data-src="T">T型</trans>}}{<trans\; data-src="\prod ">\prod </trans>}_{\mathrm{<trans\; data-src="i">我</trans>}<trans\; data-src="\in ">\in </trans>\mathrm{<trans\; data-src="T">T型</trans>}}{\mathrm{<trans\; data-src="\theta ">\theta </trans>}}_{\mathrm{<trans\; data-src="i">我</trans>}}<trans\; data-src=".">.</trans>$

低于${\mathrm{<trans\; data-src="p">第页</trans>}}_{<trans\; data-src="\{">\{</trans>\mathrm{<trans\; data-src="1">1</trans>}<trans\; data-src=",">，</trans><trans\; data-src="\dots ">\dots </trans><trans\; data-src=",">，</trans>\mathrm{<trans\; data-src="n">n个</trans>}<trans\; data-src="\}">\}</trans>}<trans\; data-src="\ne ">\ne </trans>\mathrm{<trans\; data-src="0">0</trans>}$，我们建立了关于$\mathrm{<trans\; data-src="P">P（P）</trans>}<trans\; data-src=",">，</trans>$因此，上述函数是某种概率分布的拉普拉斯变换$\mathrm{<trans\; data-src="\lambda ">\lambda </trans>}\mathrm{<trans\; data-src=">">></trans>}\mathrm{<trans\; data-src="0">0</trans>}<trans\; data-src=",">，</trans>$从而刻画了上所有可无限分的多元伽马分布${<trans\; data-src="R">R（右）</trans>}^{\mathrm{<trans\; data-src="n">n个</trans>}}<trans\; data-src=".">.</trans>$