Due to the importance of generalized order statistics (GOS) in many branches of Statistics, a wide interest has been shown in investigating stochastic comparisons of GOS. In this article, we study the likelihood ratio ordering of $p$-spacings of GOS, establishing some flexible and applicable results. We also settle certain unresolved related problems by providing some useful lemmas. Since we do not impose restrictions on the model parameters (as previous studies did), our findings yield new results for comparison of various useful models of ordered random variables including order statistics, sequential order statistics, $k$-record values, Pfeifer's record values, and progressive Type-II censored order statistics with arbitrary censoring plans. Some results on preservation of logconvexity properties among spacings are provided as well.

由于广义顺序统计 (GOS) 在统计学的许多分支中的重要性，人们对研究 GOS 的随机比较表现出广泛的兴趣。在本文中，我们研究了GOS的$p$间距的似然比排序，建立了一些灵活适用的结果。我们还通过提供一些有用的引理来解决某些未解决的相关问题。由于我们没有对模型参数施加限制（正如之前的研究所做的那样），我们的发现产生了新的结果，用于比较有序随机变量的各种有用模型，包括顺序统计、顺序顺序统计、$k$- 记录值、Pfeifer 的记录值和具有任意审查计划的渐进式 II 类审查订单统计数据。还提供了关于保持间距之间的对数凸性的一些结果。