FGM Copula下相依异质样本二阶顺序统计量的随机比较
Stochastic Comparison of Second-Order Statistics from Dependent and Heterogeneous Samples under FGM Copula
DOI: 10.12677/pm.2025.151028, PDF,   
作者: 王颢睿：西北师范大学数学与统计学院，甘肃 兰州
关键词: 二阶顺序统计量；FGM Copula；随机序；Second-Order Statistics； FGM Copula； Stochastic Orders
摘要: 本文主要研究了FGM Copula相依下随机变量二阶顺序统计量的随机比较，给出了二阶顺序统计量之间普通随机序、增凸序与增凹序关系成立的充分条件，并通过数值例子说明了主要结论。
Abstract: This paper investigates the stochastic comparison of second-order statistics from dependent random samples with FGM Copula. Sufficient conditions are established on the usual stochastic order, the increasing convex order and the increasing concave order for the second-order statistic. And some numerical examples are provided to illustrate the theoretical results.
文章引用：王颢睿. FGM Copula下相依异质样本二阶顺序统计量的随机比较[J]. 理论数学, 2025, 15(1): 259-266. https://doi.org/10.12677/pm.2025.151028

参考文献

[1] David, H.A. and Nagaraja, H.N. (2004) Order Statistics. Wiley.
[2] Balakrishnan, N. and Rao, C.R. (1998) Order Statistics: Theory & Methods. Elsevier.
[3] Zhao, P. and Balakrishnan, N. (2012) Stochastic Comparisons of Largest Order Statistics from Multiple-Outlier Exponential Models. Probability in the Engineering and Informational Sciences, 26, 159-182. [Google Scholar] [CrossRef] 
[4] Torrado, N. (2015) On Magnitude Orderings between Smallest Order Statistics from Heterogeneous Beta Distributions. Journal of Mathematical Analysis and Applications, 426, 824-838. [Google Scholar] [CrossRef] 
[5] Hazra, N.K., Kuiti, M.R., Finkelstein, M. and Nanda, A.K. (2017) On Stochastic Comparisons of Maximum Order Statistics from the Location-Scale Family of Distributions. Journal of Multivariate Analysis, 160, 31-41. [Google Scholar] [CrossRef] 
[6] Balakrishnan, N., Haidari, A. and Barmalzan, G. (2015) Improved Ordering Results for Fail-Safe Systems with Exponential Components. Communications in Statistics—Theory and Methods, 44, 2010-2023. [Google Scholar] [CrossRef] 
[7] Cai, X., Zhang, Y. and Zhao, P. (2016) Hazard Rate Ordering of the Second-Order Statistics from Multiple-Outlier PHR Samples. Statistics, 51, 615-626. [Google Scholar] [CrossRef] 
[8] Navarro, J. (2021) Introduction to System Reliability Theory. Springer.
[9] Zhang, T., Zhang, Y. and Zhao, P. (2020) Comparisons on Largest Order Statistics from Heterogeneous Gamma Samples. Probability in the Engineering and Informational Sciences, 35, 611-630. [Google Scholar] [CrossRef] 
[10] Kundu, P., Kundu, A. and Hawlader, B. (2023) Stochastic Comparisons of Largest Claim Amounts from Heterogeneous Portfolios. Statistica Neerlandica, 77, 497-515. [Google Scholar] [CrossRef] 
[11] Zhang, Y., Cai, X., Zhao, P. and Wang, H. (2018) Stochastic Comparisons of Parallel and Series Systems with Heterogeneous Resilience-Scaled Components. Statistics, 53, 126-147. [Google Scholar] [CrossRef] 
[12] Yan, R. and Niu, J. (2023) Stochastic Comparisons of Second-Order Statistics from Dependent and Heterogenous Modified Proportional Hazard Rate Observations. Statistics, 57, 328-353. [Google Scholar] [CrossRef] 
[13] Sriboonchitta, S. and Kreinovich, V. (2018) Why Are FGM Copulas Successful? A Simple Explanation. Advances in Fuzzy Systems, 2018, 1-5. [Google Scholar] [CrossRef] 
[14] Shih, J. and Emura, T. (2018) Likelihood-Based Inference for Bivariate Latent Failure Time Models with Competing Risks under the Generalized FGM Copula. Computational Statistics, 33, 1293-1323. [Google Scholar] [CrossRef] 
[15] Sha, N. (2021) A Copula Approach of Reliability Analysis for Hybrid Systems Reliability: Theory & Applications.
https://www.gnedenko.net/Journal/2021/012021/RTA_1_2021-20.pdf
[16] Fang, R. and Wang, B. (2020) Stochastic Comparisons on Sample Extremes from Independent or Dependent Gamma Samples. Statistics, 54, 841-855. [Google Scholar] [CrossRef] 
[17] Wang, B. and Fang, R. (2021) Stochastic Comparisons on Extreme Order Statistics from Observations Associated by FGM Copula. Communications in Statistics—Theory and Methods, 52, 3492-3510. [Google Scholar] [CrossRef] 
[18] Li, H. and Li, X. (2013) Stochastic Orders in Reliability and Risk. Springer.
[19] Nelsen, R.B. (2006) An Introduction to Copula. Springer.
[20] Pledger, G. and Proschan, F. (1971) Comparisons of Order Statistics and of Spacings from Heterogeneous Distributions. In: Optimizing Methods in Statistics, Elsevier, 89-113.

为你推荐