The maximum likelihood estimator (MLE) of Gini-Simpson’s diversity index (GS) is widely used but suffers from large bias when the number of species is large or infinite. We propose a new estimator of the GS index and show its unbiasedness. Asymptotic normality of the proposed estimator is established when the number of species in the population is finite and known, finite but unknown, and infinite. Simulations demonstrate advantages of our estimator over the MLE, and a real example for the extinction of dinosaurs endorses the use of our approach. Mathematics Subject Classification (MSC) codes is 60E05, which refers to distributions: general theory.

中文翻译：

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新的多样性估算器

Gini-Simpson多样性指数（GS）的最大似然估计器（MLE）已被广泛使用，但是当物种数很大或无限时，会遭受较大的偏差。我们提出了GS指数的新估计量，并显示了其无偏性。当种群中的物种数量有限且已知，有限但未知且无限时，将建立拟议估计量的渐近正态性。模拟显示了我们的估计器相对于MLE的优势，而恐龙灭绝的一个真实例子则支持使用我们的方法。数学学科分类（MSC）代码是60E05，它表示分布：一般理论。