The root density of plants with depth follows exponential or the Lindley distribution in the presence of outliers generated from a uniform distribution. In this article, we estimate the parameters of the Lindley distribution in the presence of outliers generated from a uniform distribution based on the moment, maximum likelihood, least squares, weighted least squares, percentile, Cramer–von-Mises, and Anderson–Darling methods and mixture estimator of moment and maximum likelihood. These methods of estimation are compared. Also, the estimators of the parameters of Lindley-uniform contaminated distribution are compared with the corresponding estimators of exponential-uniform contaminated distribution, which was presented by Dixit and Nasiri, Metron, 59(3–4), 187–198 (2001). Furthermore, an analysis of an actual example of the root length of plants is presented for illustrative purposes. It is concluded that the Lindley-uniform contaminated distribution is more appropriate than the exponential-uniform contaminated distribution to model the root density of plants.

中文翻译：

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存在异常值时植物根系密度分布参数的比较估计

在存在由均匀分布生成的异常值的情况下，具有深度的植物的根密度遵循指数分布或 Lindley 分布。在本文中，我们根据矩、最大似然、最小二乘法、加权最小二乘法、百分位数、Cramer-von-Mises 和 Anderson-Darling 方法估计了存在从均匀分布生成的异常值的情况下的 Lindley 分布的参数和矩和最大似然的混合估计器。比较了这些估计方法。此外，将 Lindley 均匀污染分布参数的估计量与 Dixit 和 Nasiri、Metron提出的指数均匀污染分布的相应估计量进行了比较。, 59(3–4), 187–198 (2001)。此外，出于说明目的，还提供了对植物根长度的实际示例的分析。得出的结论是，林德利均匀污染分布比指数均匀污染分布更适合模拟植物的根系密度。