量測生物多樣性有許多指標，其中Hill指標族利用位階整合了物種數、熵指標以及Simpson指標，且具有許多重要的優點，因此Hill指標族已經是目前生態領域上最廣為採用的生物多樣性指標族。
本文著重於在區塊資料下，Hill指標族的估計，並且與最大概似估計量比較。最大概似估計量雖較穩定，但在偏差的部分表現不佳，有嚴重低估的情況發生，需要提高抽取區塊數才有辦法稍微解決；本文建議之估計量利用Good-Turing (1953, 2000) 的頻率理論推倒得新的估計方法，以改善最大概似估計量低估的情形，並且發現在抽取區塊數相對於物種數小的情況下，對於誤差已有良好的表現。另外針對所討論的估計量提出變異數估計，因為傳統的拔靴方法是將樣本進行重複抽取，但在此種資料類型下，便會將出現機率較低的物種視為不存在，亦即無法透過樣本對母體作推論，因此提出修正後的拔靴方法來取得更精準的標準差估計值。對於兩種估計量以電腦進行模擬並討論估計結果，並利用實例分析以解釋實務上的應用。為求相關研究者使用此程式的便利性，以上方法已由R語言撰寫為網路互動應用程式ChaoHill-Online。

[1] Chao, A. (1984). Nonparametric estimation of the number of classes in a population. Scandinavian Journal of Statistic, 11, 265-270.
[2] Chao, A. and Jost, L. (2012). Coverage-based rarefaction and extrapolation: standardizing samples by completeness rather than size. Ecology, 52, 2533-2547.
[3] Chao, A. and Jost, L. (2014). Estimating diversity profile via discovery rates of new species. Manuscript.
[4] Chao, A. and Shen, T. J. (2003). Nonparametric estimation of Shannon's index of diversity when there are unseen species. Environmental and Ecological Statistics, 10, 429-443.
[5] Chao, A. and Shen, T. J. (2010). Program SPADE (species prediction and diversity estimation). Program and user's guide published at http://chao.stat.nthu.edu.tw.
[6] Chao, A., Wang Y. T., and Jost, L. (2013) Entropy and the species accumulation curve: a novel entropy estimator via discovery rates of new species. Methods in Ecology and Evolution, 4, 1091-1100.
[7] Chiu, C. H., Wang, Y, T., Walthers B. A., Chao, A. A improved non-parametric lower bound of species richness via the Good-Turing frequency formulas. Biometrics, in press.
[8] Efron, B. (1979) Bootstrap Methods: Another Look at the Jackknife. The Annals of Statistics, 1-26.
[9] Good, I. J. (1953). The population frequencies of species and the estimation of population parameters. Biometrika, 10, 439-443.
[10] Good, I. J. (2000). Turing's anticipation of empirical bayes in connection with the cryptanalysis of the naval enigma. Journal of Statistical Computation and Simulation, 66, 101-111.
[11] Haas, P. J., Liu, Y, Stokes, L. (2006) An estimator of number of species from quadrat sampling. Biometrics, 62, 135-141.
[12] Hill, M. (1973) Diversity and evenness: A unifying notation and its consequences. Ecology, 54, 427-432.
[13] Horvitz, D. G., Thompson, D. J. (1952) A generalization of sampling without replacement from a finite universe. Journal of American Statistical Association, 47, 663-685.
[14] Jost, L. (2006) Entropy and diversity. Oikos, 113, 363-375.
[15] MacArthur, R. H. (1965) Patterns of species diversity. Biological Reviews, 40, 510-533.
[16] Miller, G. A. (1954) Note on the basis of information estimates. Information theory in Psychology, 95-100.
[17] Murphy J., Nagorskaya L., Smith Jim (2001) Abundance and diversity of aquatic macroinvertebrate communities in lakes exposed to Chernobyl-derived ionising radiation. Journal of Environmental Radioactivity 102 (7): 688-694.
[18] Patil, G. P., Taillie, C. (1982) Diversity as a concept and its measurement. Journal of American Statistical Association, 77, 548-561.
[19] Quenouille, M. (1949) Approximate tests of correlation in time series. Journal of the Royal Statistical Society, 11, 68-84.
[20] Sannon, C. E. (1948) The mathematical theory of communication. Bell System Technical Journal, 27, 379-423.
[21] Simpson, E. H. (1949) Measurement of diversity. Nature, 163, 688.
[22] Zahl, S. (1977) Jackknifing an index of diversity. Ecology, 58, 907-913.
[23] 趙蓮菊, 邱春火, 王怡婷, 謝宗震, 馬光輝 (2013). 仰觀宇宙之大，俯察品類之盛：如何量化生物多樣性. Journal of the Chinese Statistical Association, 51, 8-53.
[24] 王怡婷 (民 100) Hill數值指標與相似度指標的統計估計 Statistical estimation of Hill numbers and similarity index 趙蓮菊指導 新竹市國立清華大學統計學研究所博士論文.
[25] 李孝寬 (民100) 物種曲線拔靴標準差修正法模擬分析與軟體開發 A simulation study and software development of the bootstrap standard deviation for species accumulation curve 趙蓮菊指導 新竹市國立清華大學統計學研究所碩士論文
[26] 周三童 (民102) 區塊抽樣之熵指標估計 Estimation of Shannon Entropy in Quadrat Sampling 趙蓮菊指導 新竹市國立清華大學統計學研究所碩士論文