|
|
基于记录值的逆威布尔分布参数统计推断
|
Abstract:
本文基于下记录值样本，研究了两参数逆威布尔分布模型的点估计和区间估计问题。基于构造的服从卡方分布的枢轴量导出了参数的逆矩估计，同时得到了形状参数的传统等尾置信区间和最短置信区间以及形状参数和尺度参数的联合置信域，最后通过数值实例将得到的区间和已有文献基于构造的服从F分布的枢轴量得到的区间进行比较以说明本文方法的优良性。
In this paper, point estimation and confidence intervals estimation of inverse Weibull distribution model with two parameters are studied based on the sample of lower record values. The inverse moment estimator of parameters is derived based on the structure of pivotal quantities subject to the chi-square distribution, and at the same time, the traditional equal tailed confidence interval and the shortest confidence interval of shape parameter, as well as the joint confidence field of shape and scale parameters, are obtained. Finally, a numerical example is given to compare the obtained intervals with the obtained intervals based on the structure of pivot quantities subject to F distribution in the existing literature, so as to illustrate the superiority of the method in this paper.
| [1] | Chandler, K.N. (1952) The Distribution and Frequency of Record Values. Journal of the Royal Statistical Society: Series B (Methodological), 14, 220-228.
https://doi.org/10.1111/j.2517-6161.1952.tb00115.x |
| [2] | Ahsanullah, M. (1995) Record Statistics. Nova Science Publishers Commack, New York. |
| [3] | Arnold, B.C., Balakrishnan, N. and Nagaraja, H.N. (1998) Records. Wiley, New York.
https://doi.org/10.1002/9781118150412 |
| [4] | Wang, B.X. and Ye, Z.-S. (2015) Inference on the Weibull Distribution Based on Record Values. Computational Statistics and Data Analysis, 83, 26-36. https://doi.org/10.1016/j.csda.2014.09.005 |
| [5] | 罗嘉成, 陈勇明. 记录值样本下极值分布的统计推断[J]. 统计与决策, 2017(18): 10-12. |
| [6] | Keller, A.Z., Kamath, A.R.R. and Perera, U.D. (1982) Reliability Analysis of CNC Machine Tools. Reliability Engineering, 3, 449-473. https://doi.org/10.1016/0143-8174(82)90036-1 |
| [7] | Asgharzadeh, A., Abdi, M. and Nadarajah, S. (2016) Interval Estimation for Gumbel Distribution Using Climate Records. Bulletin of the Malaysian Mathematical Sciences Society, 39, 257-270.
https://doi.org/10.1007/s40840-015-0185-2 |
| [8] | Sultan. K.S. (2010) Record Values from the Inverse Weibull Lifetime Model: Different Methods of Estimation. Intelligent Information Management, 2, 631-636. https://doi.org/10.4236/iim.2010.211072 |
| [9] | El-Din, M.M.M., Riad, F.H. and El-Sayed, M.A. (2014) Statistical Inference and Prediction for the Inverse Weibull Distribution Based On Record Data. Journal of Statistics Applications & Probability, 3, 171-177.
https://doi.org/10.12785/jsap/030207 |
| [10] | Lee, M.Y. (2018) On Characterizations of the Inverse Weibull Distribution Based on Record Values. Journal of Applied Mathematics & Informatics, 36, 429-433. |
| [11] | Pak, A. and Dey, S. (2019) Statistical Inference for the Power Lindley Model Based on Record Values and Inter-Record Times. Journal of Computational and Applied Mathematics, 347, 156-172.
https://doi.org/10.1016/j.cam.2018.08.012 |
| [12] | Pak, A., Jafari, A.A. and Khoolenjani, N.B. (2020) On Reliability in a Multicomponent Stress-Strength Generalized Rayleigh Model Based on Record Values. Journal of Testing and Evaluation, 48, No. 6.
https://doi.org/10.1520/JTE20170732 |
| [13] | 蒋福坤, 刘正春. 指数分布参数的最短区间估计[J]. 数理统计与管理, 2004, 23(3): 43-45+10. |
| [14] | Maswadah, M. (2003) Conditional Confidence Interval Estimation for the Inverse Weibull Distribution Based on Censored Generalized Order Statistics. Journal of Statistical Computation and Simulation, 73, 887-898.
https://doi.org/10.1080/0094965031000099140 |
