生物多樣性 (Biodiversity) 指的是地球上所有動植物、微生物，及其所有的基因、環境所構成的生態系，現今世界人口已突破65億大關，人口的激增造成糧食需求大增，人類對地表不斷的開發以及過度利用資源，使得生態系遭受破壞，影響生物生存空間，而生態系惡化也使生物多樣性銳減，進而造成物種的滅絕而導致基因消失；據估計，目前世界上每天滅絕的物種超過100種；有鑑於此，世界各國已漸漸意識到生物多樣性之重要性，在地區性的開發或是生態保育政策評估之時，都需要適當的評估其生物多樣性。
本文探討單一地區物種的多樣性，可藉由一些量化的指標來表示其物種的豐富程度，生態學家較常使用的指標有Shannon熵指標、Simpson指標以及物種數。其中Shannon熵指標是生態學家較常用的指標，而Hill (1973) 提出的Hill指標族，則可以藉由對優勢種或稀有種的加權程度做調整，來決定多樣性的指標；本文以探討Shannon熵指標及Hill指標族的各種估計量表現為主。
估計的方法，包含最大概似估計量、泰勒展式修正最大概似估計量、Horvitz-Thompson估計量及一階摺刀法；在此，進而使用二階摺刀法、三階摺刀法，比較各估計量之優缺點；一個估計量之優劣，除了考量其偏誤是否夠小，也應一併考量其變異數是否穩定；所以在此同時考量這兩部分，以樣本均方根誤差來評估估計量之優劣，並進而模擬各種常見的生態機率模型，配合不同的抽樣數，比較各估計量之表現，最後輔以實例說明。

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