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Pure Mathematics 2025
基于改进比例反失效率模型有限混合总体的随机性质
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Abstract:
在大数据时代，总体往往呈现出显著的异质性特点。本文借助混合模型来刻画了多个同质个体构成总体的异质性。我们基于改进比例反失效率模型的参数来体现种群中的信息，探讨了改进比例反失效率模型构成有限混合模型的统计性质，结合矩阵链优序或向量的优化序和T转换矩阵，研究了有限混合模型参数和混合比例的随机性质，给出了两组异质有限混合总体普通随机序成立的充分条件，丰富了异质有限混合总体的随机比较理论。
With the advent of the big data era, populations frequently display distinct heterogeneity characteristics. This paper uses mixture models to characterize the heterogeneity of populations composed of multiple homogeneous individuals. Based on the parameters of a modified proportional reversed hazard rate model, we incorporate information from the population and explore the statistical properties of a finite mixture model formed by the modified proportional reversed hazard rate model. By combining matrix chain optimization or the optimization sequence of vectors with the T-transformation matrix, we study the stochastic properties of the finite mixture model’s parameters and mixing proportions. Sufficient conditions for the establishment of ordinary stochastic order for two heterogeneous finite mixture populations are provided, enriching the theory of stochastic comparisons for heterogeneous finite mixture populations.
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