Using the sample maximum to estimate the parameters of the underlying distribution
Using the sample maximum to estimate the parameters of the underlying distribution
复制标题
DOI：
10.1371/journal.pone.0215529
复制
发表时间：
2019-04-25
期刊：
影响因子：
3.7
通讯作者：
Kolba, Tiffany N.
中科院分区：
文献类型：
--
作者：
Capaldi, Alex;Kolba, Tiffany N.
当唯一已知的信息是样本最大值的样本时，我们提出了指数分布和正态分布参数的新估计;即，已知信息由m个值的样本组成，每个值是从基础指数或正态分布中抽取的n个独立随机变量的样本的最大值。我们使用极值理论分析估计的准确性和精度，以及通过模拟的抽样分布。对于指数分布，均值的估计是无偏的，其方差随着m或n的增加而减小。同样，对于正态分布，我们证明了均值的估计有可忽略的偏差，方差的估计是无偏的。虽然正态分布的估计量的方差随着m（样本最大值的数量）的增加而减少，但方差随着n（计算最大值的样本大小）的增加而增加。我们应用我们的方法来估计显花植物拟南芥中的花粉管的平均长度，其中已知的生物信息符合我们的背景下的样本的样本极大值。
We propose novel estimators for the parameters of an exponential distribution and a normal distribution when the only known information is a sample of sample maxima; i.e., the known information consists of a sample of m values, each of which is the maximum of a sample of n independent random variables drawn from the underlying exponential or normal distribution. We analyze the accuracy and precision of the estimators using extreme value theory, as well as through simulations of the sampling distributions. For the exponential distribution, the estimator of the mean is unbiased and its variance decreases as either m or n increases. Likewise, for the normal distribution, we show that the estimator of the mean has negligible bias and the estimator of the variance is unbiased. While the variance of the estimators for the normal distribution decreases as m, the number of sample maxima, increases, the variance increases as n, the sample size over which the maximum is computed, increases. We apply our method to estimate the mean length of pollen tubes in the flowering plant Arabidopsis thaliana, where the known biological information fits our context of a sample of sample maxima.