Tong Y L
Biometrics. 1983 Dec;39(4):999-1008.
In the area of ecological research the study of species diversity of a community or population seems to have been fully developed. However, the problem of how the distributions and expectations of the sample diversity indices are affected by the population diversity has received little attention. In this paper we show that if the diversities of the communities can be partially ordered through majorization as proposed by Solomon [1979, in Ecological Diversity in Theory and Practice, J. F. Grassle, G. P. Patil, W. K. Smith and C. Taillie (eds), 29-35, Fairland, Maryland: International Co-operative Publishing House], and if the sample sizes remain the same, then the sample diversity indices can be stochastically ordered when the samples are selected at random from the communities either with or without replacement. We also show that, when the sample size becomes large, the sample diversity indices are asymptotically normally distributed. These results can be applied for comparing the diversities of the communities on the basis of the samples, and they yield certain desirable monotonicity properties.
在生态研究领域，群落或种群的物种多样性研究似乎已经相当完善。然而，样本多样性指数的分布和期望如何受到种群多样性的影响这一问题却很少受到关注。在本文中，我们表明，如果群落的多样性能够像所罗门[1979年，载于《理论与实践中的生态多样性》，J. F. 格拉斯勒、G. P. 帕蒂尔、W. K. 史密斯和C. 塔利（编），第29 - 35页，费尔兰，马里兰州：国际合作出版公司]所提出的那样通过优化排序进行部分排序，并且样本量保持不变，那么当从群落中随机抽取样本（有放回或无放回）时，样本多样性指数可以进行随机排序。我们还表明，当样本量变大时，样本多样性指数渐近服从正态分布。这些结果可用于基于样本比较群落的多样性，并且它们具有某些理想的单调性性质。
