基于改进比例反失效率模型有限混合总体的随机性质
Stochastic Properties of Finite Mixture Population Based on the Modified Proportional Reversed Hazard Rate Model
DOI: 10.12677/pm.2025.152044, PDF,    国家自然科学基金支持
作者: 郭丽娜：西北师范大学数学与统计学院，甘肃 兰州
关键词: 有限混合模型；改进比例反失效率模型；随机序；链优序；Finite Mixture Model； Modified Proportional Reversed Hazard Rate Model； Stochastic Order； Chain Majorization Order
摘要: 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。
Abstract: 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.
文章引用：郭丽娜. 基于改进比例反失效率模型有限混合总体的随机性质[J]. 理论数学, 2025, 15(2): 39-48. https://doi.org/10.12677/pm.2025.152044

参考文献

[1] Amini-Seresht, E. and Zhang, Y. (2017) Stochastic Comparisons on Two Finite Mixture Models. Operations Research Letters, 45, 475-480. [Google Scholar] [CrossRef] 
[2] Finkelstein, M. (2008) Failure Rate Modelling for Reliability and Risk. Springer Science & Business Media.
[3] Cha, J.H. and Finkelstein, M. (2013) The Failure Rate Dynamics in Heterogeneous Populations. Reliability Engineering & System Safety, 112, 120-128. [Google Scholar] [CrossRef] 
[4] Hazra, N.K. and Finkelstein, M. (2018) On Stochastic Comparisons of Finite Mixtures for Some Semiparametric Families of Distributions. TEST, 27, 988-1006. [Google Scholar] [CrossRef] 
[5] Albabtain, A.A., Shrahili, M., Al-Shehri, M.A. and Kayid, M. (2020) Stochastic Comparisons of Weighted Distributions and Their Mixtures. Entropy, 22, Article 843. [Google Scholar] [CrossRef] [PubMed]
[6] Barmalzan, G., Hosseinzadeh, A.A. and Balakrishnan, N. (2021) Dispersion and Variability Orders of Mixture Exponential Distributions and Their Sample Spacings, and Some Associated Characterizations. Communications in Statistics—Theory and Methods, 51, 8657-8670. [Google Scholar] [CrossRef] 
[7] Barmalzan, G., Kosari, S. and Balakrishnan, N. (2020) Orderings of Finite Mixture Models with Location-Scale Distributed Components. Probability in the Engineering and Informational Sciences, 36, 461-481. [Google Scholar] [CrossRef] 
[8] Panja, A., Kundu, P. and Pradhan, B. (2021) On Stochastic Comparisons of Finite Mixture Models. Stochastic Models, 38, 190-213. [Google Scholar] [CrossRef] 
[9] Nadeb, H. and Torabi, H. (2020) New Results on Stochastic Comparisons of Finite Mixtures for Some Families of Distributions. Communications in Statistics—Theory and Methods, 51, 3104-3119. [Google Scholar] [CrossRef] 
[10] Shojaee, O. and Babanezhad, M. (2022) On Some Stochastic Comparisons of Arithmetic and Geometric Mixture Models. Metrika, 86, 499-515. [Google Scholar] [CrossRef] 
[11] Bhakta, R., Kundu, P., Kayal, S. and Alizadeh, M. (2024) Stochastic Orderings between Two Finite Mixtures with Inverted-Kumaraswamy Distributed Components. Mathematics, 12, Article 852. [Google Scholar] [CrossRef] 
[12] Bhakta, R., Majumder, P., Kayal, S. and Balakrishnan, N. (2023) Stochastic Comparisons of Two Finite Mixtures of General Family of Distributions. Metrika, 87, 681-712. [Google Scholar] [CrossRef] 
[13] Yan, R., Zhang, J. and Zhang, Y. (2021) Optimal Allocation of Relevations in Coherent Systems. Journal of Applied Probability, 58, 1152-1169. [Google Scholar] [CrossRef] 
[14] Zhang, J., Yan, R. and Zhang, Y. (2022) Reliability Analysis of Fail-Safe Systems with Heterogeneous and Dependent Components Subject to Random Shocks. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 237, 1073-1087. [Google Scholar] [CrossRef] 
[15] Zhang, J. and Zhang, Y. (2023) Stochastic Comparisons of Relevation Allocation Policies in Coherent Systems. TEST, 32, 865-907. [Google Scholar] [CrossRef] 
[16] Lu, B., Zhang, J. and Yan, R. (2021) Optimal Allocation of a Coherent System with Statistical Dependent Subsystems. Probability in the Engineering and Informational Sciences, 37, 29-48. [Google Scholar] [CrossRef] 
[17] Zhang, J., Yan, R. and Zhang, Y. (2023) Stochastic Comparisons of Largest Claim Amount from Heterogeneous and Dependent Insurance Portfolios. Journal of Computational and Applied Mathematics, 431, Article ID: 115265. [Google Scholar] [CrossRef] 
[18] Guo, M., Zhang, J. and Yan, R. (2024) Stochastic Comparisons of Second Largest Order Statistics with Dependent Heterogeneous Random Variables. Communications in Statistics—Theory and Methods. [Google Scholar] [CrossRef] 
[19] Zhang, J., Guo, Z., Niu, J. and Yan, R. (2024) Increasing Convex Order of Capital Allocation with Dependent Assets under Threshold Model. Statistical Theory and Related Fields, 8, 124-135. [Google Scholar] [CrossRef] 
[20] Balakrishnan, N., Barmalzan, G. and Haidari, A. (2018) Modified Proportional Hazard Rates and Proportional Reversed Hazard Rates Models via Marshall-Olkin Distribution and Some Stochastic Comparisons. Journal of the Korean Statistical Society, 47, 127-138. [Google Scholar] [CrossRef] 
[21] Shaked, M. and Shanthikumar, J.G. (2007) Stochastic Orders. Springer.
[22] Marshall, A.W. (1979) Inequalities: Theory of Majorization and Its Applications. Springer.
[23] Balakrishnan, N., Haidari, A. and Masoumifard, K. (2015) Stochastic Comparisons of Series and Parallel Systems with Generalized Exponential Components. IEEE Transactions on Reliability, 64, 333-348. [Google Scholar] [CrossRef] 

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