Stochastic Properties Of Mixed Semi-parametric And SPRH Semi-parametric Models

Data collected in econometrics、industrial engineering、insurance actuarial science and many other fields are often heterogeneous.The finite mixture model is an effective tool for modeling the lifetime distribution of a random sample from heterogeneous populations.In this paper,we study the influence mechanism of mixed parameters and heterogeneous parameters on the populational distribution under the semiparametric framework.The conclusions show that under the general semi-parametric mixed model,when the majorization order between the two sets of mixed proportional vectors together with the weakly supermajorization order between parameter vectors imply the usual stochastic ordering between the two mixed distributions.Under the SPHR model,when the majorization order between the two sets of mixed proportional vectors together with the weakly supermajorization order between shape(scale)parameter vectors imply the usual stochastic ordering between the two mixed distributions.Star order is a random partial order that describes the degree of shape bias of a random variable.Under the SPRH model,this paper further studies the effects of scale parameters and shape parameters on the order statistic distribution.The conclusions show that when there are no restrictions on the scale parameters,the life of the parallel system with component lifetime obeying the homogeneous SPRH model is faster than that of the parallel system with the component lifetime obeying the non-homogeneous SPRH model.For the independent multiple-outlier SPRH model,the star ordering between the corresponding maximum order statistic and minimum order statistic are given respectively.The research results promote and improve the results in the existing literature,which has important theoretical significance.