Abstract

The half logistic-geometric (HLG) distribution derived here is a simple distribution with interesting properties and is therefore a useful distribution for analyzing lifetime data. Algorithm is derived for the computation of single and product moments of order statistics from this distribution. These recurrence relations enable the computation of means, variances and covariances of all order statistics for all sample size in a simple and efficient way. The results are of great importance in determining the best linear unbiased estimator of the scale parameter of a scaled-HLG distribution, and those of parameters of the more general location-scale HLG distribution based on complete and Type-II censored samples. Finally, an example is presented to illustrate the developed results.

摘要

此处导出的半逻辑几何 (HLG) 分布是一种具有有趣属性的简单分布，因此是分析寿命数据的有用分布。推导出用于从该分布计算单个和产品阶矩统计量的算法。这些递归关系能够以简单有效的方式计算所有样本大小的所有顺序统计量的均值、方差和协方差。结果对于确定缩放 HLG 分布的尺度参数的最佳线性无偏估计量以及基于完整和 II 类删失样本的更一般位置尺度 HLG 分布的参数的估计量具有重要意义。最后，给出了一个例子来说明开发的结果。