The order statistics (OSs) arise in both practical and theoretical aspects including goodness-of-fit tests, characterizations of probability distributions and some estimation approaches such as the L-moments method. Most of these instances are connected with moments of OSs. The records and $k$-record statistics, also called $k$th record values in the literature, are other important topics related to the OSs. This kind of data appears in some practical circumstances, e.g. shock models, industrial stress testing and meteorological data analysis. This paper deals with deriving recurrence relations for the single and the product moments of OSs as well as $k$-record values from the complementary beta (CB) distribution defined by Jones (2002). The CB model, as a distribution on the unit interval, is more flexible than the well-known beta distribution in problems involving moments of OSs. This fact suggests that the former distribution can be employed rather than the latter when OSs are of the main interest. The results obtained are applied on four real data sets for the issues of parameter estimation as well as providing a visual inspection for goodness-of-fit of the CB model.

顺序统计（OS）出现在实践和理论两个方面，包括拟合优度检验，概率分布的表征和一些估计方法，例如L矩法。这些实例中的大多数与操作系统的时刻有关。记录和$ķ$-记录统计信息，也称为 $ķ$文献中的记录值是与OS相关的其他重要主题。这种数据出现在某些实际情况下，例如冲击模型，工业压力测试和气象数据分析。本文讨论了OS的单一时刻和产品时刻的推导递归关系，以及$ķ$-记录Jones（2002）定义的互补beta（CB）分布的值。CB模型作为单位间隔上的分布，在涉及OS矩的问题上比众所周知的beta分布更灵活。这一事实表明，当主要关注操作系统时，可以采用前一种发行版，而不能采用后者。将获得的结果应用于四个实际数据集，以解决参数估计问题，并为CB模型的拟合优度提供视觉检查。