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Concomitants of Generalized Order Statistics from Bivariate Cambanis Family: Some Information Measures
Bulletin of the Iranian Mathematical Society ( IF 0.7 ) Pub Date : 2021-04-05 , DOI: 10.1007/s41980-021-00532-8
Mohamed Ahmed Abd Elgawad , Haroon Mohamed Barakat , Metwally Alsayed Alawady

In this paper, we study the concomitants of m-generalized order statistics (m-GOS) from the bivariate Cambanis family as an extension of several recent papers. This study can also be applied to the model of m-dual generalized order statistics (m-DGOS) as a parallel model of m-GOS. Some information measures, namely the Shannon entropy, Kullback-Leibler (KL) distance, and Fisher information number (FIN) for the concomitants of m-GOS, are derived. Furthermore, the joint distribution of concomitants of m-GOS for this family is studied. Besides, some useful recurrence relations between moments of concomitants are obtained. Moreover, the ordinary order statistics (OOS) and an important subclass of sequential order statistics (SOS) as subclasses of m-GOS, as well as the progressive type II censored order statistics (POS) as a more general subclass of GOS, are separately discussed. Finally, an application of these results is given for bivariate generalized exponential distribution.



中文翻译:

双变量Cambanis家族的广义阶统计的伴随物:一些信息测度

在本文中,我们研究了来自双变量Cambanis家族的m广义阶次统计量(m -GOS)的伴随物,作为最近几篇论文的扩展。本研究中也可以应用到的模型-双广义顺序统计(-DGOS)作为一个并行模型-GOS。推导了一些信息量度,即香农熵,Kullback-Leibler(KL)距离和m -GOS伴随物的Fisher信息数(FIN)。此外,m伴随的联合分布-对该家庭的GOS进行了研究。此外,获得了伴随时刻之间的一些有用的递归关系。此外,普通订单统计(OOS)和顺序订单统计(SOS)的重要子类(作为m -GOS的子类),以及渐进式II型审查订单统计(POS)作为GOS的更通用的子类,分别分开讨论过。最后,给出了这些结果在双变量广义指数分布中的应用。

更新日期:2021-04-05
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