In this paper, we consider two finite mixture models (FMMs), with inverted-Kumaraswamy distributed components' lifetimes. Several stochastic ordering results between the FMMs have been obtained. Mainly, we focus on three different cases in terms of the heterogeneity of parameters. The usual stochastic order between the FMMs have been established when heterogeneity presents in one parameter as well as two parameters. In addition, we have also studied ageing faster order in terms of the reversed hazard rate between two FMMs when heterogeneity is in two parameters. For the case of heterogeneity in three parameters, we obtain the comparison results based on reversed hazard rate and likelihood ratio orders. The theoretical developments have been illustrated using several examples and counterexamples.

翻译：本文考虑两个有限混合模型（FMMs），其分量寿命服从倒置Kumaraswamy分布。我们获得了这两个FMMs之间的若干随机排序结果。主要围绕参数的异质性，研究了三种不同情形。当异质性存在于一个参数及两个参数时，建立了FMMs之间的通常随机序。此外，当异质性存在于两个参数时，还研究了基于逆风险率的老化更快序。对于三个参数存在异质性的情形，我们基于逆风险率序和似然比序得到了比较结果。通过若干实例和反例对理论发展进行了说明。