本論文主要探討在封閉模式下，具有個體異質性且個體捕取機率服從貝塔分配(Beta distribution)的離散型重複捕取實驗的母體總數估計。在有母數的方法中最大概似估計量已經行之有年，我們有興趣的是在二樣本、三樣本、四樣本的情形下，最大概似估計量是否可以解出唯一解與確切解，如果可以我們寫下確切解的形式，如果不行時我們則討論了解數值解的方法。另外針對無母數的方法，由於樣本涵蓋估計量(Chao and Tsay,1998)在貝塔-二項式的模式假設下並不適用，所以我們藉由討論二樣本、三樣本、四樣本時樣本涵蓋估計量的表現，並進一步提出修正的估計量，最後則以不同參數下的模擬來分析各種估計量的表現，並做文獻上的實例分析。

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