﻿ 广义指数分布参数变点的检验

# 广义指数分布参数变点的检验Detecting Parameters Change Points in the Generalized Exponential Distribution

Abstract: This paper proposes a likelihood ratio method and a CUSUM method to detect change points of lo-cation parameters and scale parameters in the generalized exponential distribution. A Bootstrap method is introduced to approximate the critical values of the statistics for the scale parameters change points without explicit estimation leading to the critical values of statistic not easy to cal-culate. Simulations show that the likelihood ratio method is better than the CUSUM method when detecting change points of location parameters, however, the likelihood ratio statistic can’t test change points of scale parameters. While the CUSUM method has the good performance testing two kinds of parameters change points. Combining the two methods can differentiate location pa-rameters and scale parameters change points. Finally, the validity of proposed methods is demon-strated by analyzing a set of voltage data.

[1] Gupta, R.D. and Kundu, D. (1999) Generalized Exponential Distributions. Australian and New Zealand Journal of Statistics, 41, 173-188. http://dx.doi.org/10.1111/1467-842X.00072

[2] Raqab, M.Z. (2004) Generalized Exponential Distribution Moments of Order Statistics. Statistics, 38, 29-41. http://dx.doi.org/10.1080/0233188032000158781

[3] Raqab, M.Z. and Madi, M.T. (2005) Bayesian Inference for the Generalized Exponential Distribution. Statistical Com- putation and Simulation, 75, 841-852. http://dx.doi.org/10.1080/00949650412331299166

[4] Asgharzadeh, A. (2009) Approximate MLE for the Scaled Ge-neralized Exponential Distribution under Progressive Type- II Censoring. Journal of the Korean Statistical Society, 3, 223-229.
http://dx.doi.org/10.1016/j.jkss.2008.09.004

[5] Gupta, R.D. and Kundu, D. (2001) Generalized Ex-ponential Distribution: Different Methods of Estimations. Journal of Statistical Computation and Simulation, 69, 315-337.
http://dx.doi.org/10.1080/00949650108812098

[6] Gupta, R.D. and Kundu, D. (2001) Exponentiated Exponential Family: An Alternative to Gammaand Weibull Distributions. Biometrical Journal, 43, 117-130.
http://dx.doi.org/10.1002/1521-4036(200102)43:1<117::AID-BIMJ117>3.0.CO;2-R

[7] 黄志坚, 张志华. 基于指数分布数据的可靠性变点分析[J]. 武汉理工大学学报, 2008, 30(2): 157-160.

[8] 王黎明, 王静龙. 位置参数变点的非参数检验及其渐近性质[J]. 数学年刊A辑(中文版), 2002(2): 229-234.

[9] 谭常春, 缪柏其, 惠军. 分布参数变点的非参数统计推断[J]. 中国科学技术大学学报, 2008, 38(2): 149-156.

[10] 王黎明. 双参数指数分布参数变点的统计推断[J]. 系统工程, 2004, 22(3): 106-110.

[11] 苏海军, 杨煜普, 王宇嘉. 微分进化算法的研究综述[J]. 系统工程与电子技术, 2008, 30(9): 1793-1797.

[12] Robbins, M., Gallagher, C., Lund, R., et al. (2011) Mean Shift Testing in Correlated Data. Journal of Time Series Analysis, 32, 498-511.
http://dx.doi.org/10.1111/j.1467-9892.2010.00707.x

[13] 陈占寿, 田铮. 一类厚尾随机信号平稳性的在线bootstrap监测[J]. 控制理论与应用, 2010, 27(7): 933-938.

[14] 赵春辉, 田铮, 陈占寿. 非参数模型均值函数结构变点的Bootstrap检测[J]. 数理统计与管理, 2011, 30(4): 629-638.

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