基于仿真的威布尔分布参数估计方法比较研究

A. Sajib, Sabina Sharmin, Sharmin Akter
{"title":"基于仿真的威布尔分布参数估计方法比较研究","authors":"A. Sajib, Sabina Sharmin, Sharmin Akter","doi":"10.3329/dujs.v71i1.65268","DOIUrl":null,"url":null,"abstract":"This paper aims to find efficient methods for estimating the parameters (shape =α , scale = β ) of Weibull distribution in different situations. The maximum likelihood estimation method (MLE), the median rank regression method (MRR), the least square method (LSM) and the weighted least square method (WLSM) are considered for the estimation of the parameters. The root mean square error (RMSE) criterion is used to measure the relative efficiency of the estimators experimentally (Monte Carlo simulation). From the simulation study, it is observed that the MLE produces the lowest RMSE, irrespective of all sample sizes, for decreasing hazard function(α << β ) (α is considerably smaller than β ) and roughly linear hazard function with a positive slope (α >1) . When (α >> β ) the WLSM produces the lowest RMSE for small sample sizes (n ≤ 40) but for large sample sizes it is the MLE, irrespective of all types of hazard functions. When (α ,β →1), the WLSM produces the lowest RMSE for small sample sizes (n ≤ 40) and the MLE for large sample sizes irrespective of all types of hazard functions. This pattern becomes reversed whenα and β have the larger value. Only the MLE gets stuck when the hazard function is parallel to Y − axis (α >> β ) and the WLSM is suitable in such a situation (lowest RMSE) irrespective of all sample sizes. Finally, the utility of simulation results have been illustrated by analyzing two real-life data sets.\nDhaka Univ. J. Sci. 71(1): 17-25, 2023 (Jan)","PeriodicalId":11280,"journal":{"name":"Dhaka University Journal of Science","volume":"30 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Simulation Based Comparative Study to Find Efficient Parameter Estimation Methods for Weibull Distribution\",\"authors\":\"A. Sajib, Sabina Sharmin, Sharmin Akter\",\"doi\":\"10.3329/dujs.v71i1.65268\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper aims to find efficient methods for estimating the parameters (shape =α , scale = β ) of Weibull distribution in different situations. The maximum likelihood estimation method (MLE), the median rank regression method (MRR), the least square method (LSM) and the weighted least square method (WLSM) are considered for the estimation of the parameters. The root mean square error (RMSE) criterion is used to measure the relative efficiency of the estimators experimentally (Monte Carlo simulation). From the simulation study, it is observed that the MLE produces the lowest RMSE, irrespective of all sample sizes, for decreasing hazard function(α << β ) (α is considerably smaller than β ) and roughly linear hazard function with a positive slope (α >1) . When (α >> β ) the WLSM produces the lowest RMSE for small sample sizes (n ≤ 40) but for large sample sizes it is the MLE, irrespective of all types of hazard functions. When (α ,β →1), the WLSM produces the lowest RMSE for small sample sizes (n ≤ 40) and the MLE for large sample sizes irrespective of all types of hazard functions. This pattern becomes reversed whenα and β have the larger value. Only the MLE gets stuck when the hazard function is parallel to Y − axis (α >> β ) and the WLSM is suitable in such a situation (lowest RMSE) irrespective of all sample sizes. Finally, the utility of simulation results have been illustrated by analyzing two real-life data sets.\\nDhaka Univ. J. Sci. 71(1): 17-25, 2023 (Jan)\",\"PeriodicalId\":11280,\"journal\":{\"name\":\"Dhaka University Journal of Science\",\"volume\":\"30 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-05-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Dhaka University Journal of Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3329/dujs.v71i1.65268\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dhaka University Journal of Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3329/dujs.v71i1.65268","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

本文旨在寻找在不同情况下威布尔分布参数(形状=α,尺度= β)估计的有效方法。采用极大似然估计法(MLE)、中位秩回归法(MRR)、最小二乘法(LSM)和加权最小二乘法(WLSM)对参数进行估计。采用均方根误差(RMSE)准则对估计器的相对效率进行了实验测量(蒙特卡罗模拟)。从模拟研究中可以观察到,对于降低风险函数(α 1),无论所有样本量大小,MLE都产生最低的RMSE。当(α >> β) WLSM对小样本量(n≤40)产生最低RMSE时,而对于大样本量,无论所有类型的危害函数如何,它都是最大均值。当(α,β→1)时,无论何种类型的风险函数,WLSM对小样本量(n≤40)产生的RMSE最低,对大样本量产生的MLE最低。当α和β具有较大的值时,这种模式变得相反。只有当危害函数平行于Y -轴(α >> β)时,MLE才会卡住,而无论所有样本量大小,WLSM都适用于这种情况(最低RMSE)。最后,通过对两个实际数据集的分析,说明了仿真结果的实用性。达卡大学学报(自然科学版),71(1):17- 25,2023 (1)
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Simulation Based Comparative Study to Find Efficient Parameter Estimation Methods for Weibull Distribution
This paper aims to find efficient methods for estimating the parameters (shape =α , scale = β ) of Weibull distribution in different situations. The maximum likelihood estimation method (MLE), the median rank regression method (MRR), the least square method (LSM) and the weighted least square method (WLSM) are considered for the estimation of the parameters. The root mean square error (RMSE) criterion is used to measure the relative efficiency of the estimators experimentally (Monte Carlo simulation). From the simulation study, it is observed that the MLE produces the lowest RMSE, irrespective of all sample sizes, for decreasing hazard function(α << β ) (α is considerably smaller than β ) and roughly linear hazard function with a positive slope (α >1) . When (α >> β ) the WLSM produces the lowest RMSE for small sample sizes (n ≤ 40) but for large sample sizes it is the MLE, irrespective of all types of hazard functions. When (α ,β →1), the WLSM produces the lowest RMSE for small sample sizes (n ≤ 40) and the MLE for large sample sizes irrespective of all types of hazard functions. This pattern becomes reversed whenα and β have the larger value. Only the MLE gets stuck when the hazard function is parallel to Y − axis (α >> β ) and the WLSM is suitable in such a situation (lowest RMSE) irrespective of all sample sizes. Finally, the utility of simulation results have been illustrated by analyzing two real-life data sets. Dhaka Univ. J. Sci. 71(1): 17-25, 2023 (Jan)
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信