数学季刊 >

2023 , Vol. 38 >Issue 1: 97 - 110

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2023.01.007

I型左删失下Topp–Leone分布的参数及可靠度函数的估计

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  • School of Information and Mathematics, Yangtze University, Jingzhou 434023, China
LONG Qin-yi (1998-), female, native of Jingmen, Hubei, graduate student of Yangtze University, engages in probability and statistics; XU Li-ping (1980-), female, native of Weifang, Shandong, associate professor of Yangtze University, engages in probability and statistics.

收稿日期: 2021-10-19

  网络出版日期: 2023-03-20

基金资助

Supported by National Natural Science Foundation of China (Grant No. 11901058).

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Estimates of the Parameter and Reliability Function for the Topp-Leone Distribution under Type-I Left Censoring

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  • School of Information and Mathematics, Yangtze University, Jingzhou 434023, China
LONG Qin-yi (1998-), female, native of Jingmen, Hubei, graduate student of Yangtze University, engages in probability and statistics; XU Li-ping (1980-), female, native of Weifang, Shandong, associate professor of Yangtze University, engages in probability and statistics.

Received date: 2021-10-19

  Online published: 2023-03-20

Supported by

Supported by National Natural Science Foundation of China (Grant No. 11901058).

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摘要

 Firstly, the maximum likelihood estimate and asymptotic confidence interval
of the unkown parameter for the Topp-Leone distribution are obtained under Type-I left
censored samples, furthermore, the asymptotic confidence interval of reliability function
is obtained based on monotonicity. Secondly, under different loss functions, the Bayesian
estimates of the unkown parameter and reliability function are obtained, and the expected
mean square errors of Bayesian estimates are calculated. Monte-Carlo method is used to
calculate the mean values and relative errors of the estimates. Finally, an example of life
data is analyzed by using the statistical method in this paper.

关键词：  Topp-Leone distribution; Type-I left censored samples; Maximum likelihood
estimate; Bayesian estimate

本文引用格式

龙沁怡, 徐丽平 . I型左删失下Topp–Leone分布的参数及可靠度函数的估计[J]. 数学季刊, 2023 , 38(1) : 97 -110 . DOI: 10.13371/j.cnki.chin.q.j.m.2023.01.007

Abstract

 Firstly, the maximum likelihood estimate and asymptotic confidence interval
of the unkown parameter for the Topp-Leone distribution are obtained under Type-I left
censored samples, furthermore, the asymptotic confidence interval of reliability function
is obtained based on monotonicity. Secondly, under different loss functions, the Bayesian
estimates of the unkown parameter and reliability function are obtained, and the expected
mean square errors of Bayesian estimates are calculated. Monte-Carlo method is used to
calculate the mean values and relative errors of the estimates. Finally, an example of life
data is analyzed by using the statistical method in this paper.

Key words：  Topp-Leone distribution; Type-I left censored samples; Maximum likelihood
estimate; Bayesian estimate

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