[1]林金官,王海斌,刘应安,等.基于Ⅱ型截尾样本下Rayleigh分布参数的条件置信限[J].东南大学学报(自然科学版),2001,31(2):117-122.[doi:10.3969/j.issn.1001-0505.2001.02.028]
 Lin Jinguan,Wang Haibin,Liu Yingan,et al.Conditional Confidence Intervals of the Parameters for Two-Parameter Rayleigh Distribution Based on Type-Ⅱ Censored Samples[J].Journal of Southeast University (Natural Science Edition),2001,31(2):117-122.[doi:10.3969/j.issn.1001-0505.2001.02.028]
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基于Ⅱ型截尾样本下Rayleigh分布参数的条件置信限()
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《东南大学学报(自然科学版)》[ISSN:1001-0505/CN:32-1178/N]

卷:
31
期数:
2001年第2期
页码:
117-122
栏目:
数学、物理学、力学
出版日期:
2001-03-20

文章信息/Info

Title:
Conditional Confidence Intervals of the Parameters for Two-Parameter Rayleigh Distribution Based on Type-Ⅱ Censored Samples
作者:
林金官 王海斌 刘应安 韦博成
东南大学应用数学系,南京 210096
Author(s):
Lin Jinguan Wang Haibin Liu Yingan Wei Bocheng
Department of Applied Mathematics,Southeast University, Nanjing 210096)
关键词:
Rayleigh分布 Ⅱ型截尾 条件分布 置信区间 容许限
Keywords:
Rayleigh distribution type-Ⅱcensored sample conditional distribution confidence intervals tolerance limits
分类号:
O212.2
DOI:
10.3969/j.issn.1001-0505.2001.02.028
摘要:
Rayleigh分布是很重要的寿命分布,单参数Rayleigh分布的参数推断问题在一些文献中已有讨论.本文假设寿命X服从双参数Rayleigh分布,即X有密度 f(x; μ,σ)=(2(x-μ))/σe<sup>((x-μ)2)/σ x>μ; -∞<μ<∞; σ>0 通过Ⅱ型截尾样本的前r个次序统计量:X(1)≤X(2)≤…≤X(r) (r≤n),首先推出了枢轴量Z1=((^overμ)-μ)/(( ^)/σ)1/2,Z2=(^overσ)/σ建立在可观测的辅助统计量a=(a1,a2,…,ar)(ai=(X(i)-(^overμ))/(( ^)/σ)1/2; μ,(^overσ)分别为参数μ,σ的极大似然估计)基础上的条件分布,据此得到了参数μ,σ的条件置信限(置信区间),最后,给出了p-分位点xp的置信区间和Rayleigh分布的容许限的计算方法.
Abstract:
The Rayleigh distribution is an important life distribution. For one-parameter Rayleigh distribution, the inferences of parameter have been discussed in some articles. In this paper, we let life X follow two-parameter distribution R(μ,σ),i.e. X has density f(x; μ,σ)=(2(x-μ))/σe<sup>-((x-μ)2)/σ x>μ; -∞<μ<∞; σ>0 X(1)≤X(2)≤…≤X(r) are the order statistics of a type-Ⅱ censored sample. We use MLEs of μ,σ to derive the marginal conditional distributions of pivotal quantities: Z1=((^overμ)-μ)/(( ^)/σ)1/2, Z2=(^overσ)/σ under the condition of the ancillary statistics:a=(a1,a2,…,ar) based on type-Ⅱ censored sample from R(μ,σ),where ai=(X(i)-(^overμ))/(( ^)/σ)1/2,(^overμ),(^overσ) are MLEs of μ,σ respectively. Then, we obtain conditional confidence intervals of parameters μ,σ on theobserved values of a=(a1,a2,…,ar). Finally, we give computational methods of conditional confidence limits of p-fractile xp and tolerance interval of R(μ,σ).

参考文献/References:

[1] Engelhardt M,Bain L J.Tolerance limits and confidence limits on reliability for the two-parameter exponential distribution.Technometrics,1978,20(1):37~39
[2] Lawless J F.Statsatical models and methods for lifetime data.New York:Wiley,1982.187~312
[3] Lawless J F.Confidence interval estimation for the Weibull and extreme value distributions.Technometrics,1978,20(1):355~364
[4] Kappenman R F.Conditional confidence intervals for double exponential distribution parameters.Technometrics,1975,17(1):233~235
[5] Kappenman R F.Tolerance intervals for the double exponential distribution.J Amer Statist Assoc, 1977,72(3):908~909
[6] Balakrishnan N,Culter C D.Maximum likelihood estimation of Laplace parameters based on type-Ⅱ censored sampes.In:Nagaraja H N,Sen P K,Morrison D F,eds.Statistical Theory and Application:Papers in Honor of Herbert A.David.New York:Springer,1995.45~151
[7] Childs A,Balakrishnan N.Conditional inference procedures for the Laplace distribution based on type-Ⅱ right censored samples.Statistics & Probability Letters,1996,31(1):31~39
[8] Lin Jinguan.The parameter estimations of Rayleigh distribution.Mathematical Quartly,2000,15(4):1~6

备注/Memo

备注/Memo:
作者简介:林金官,男,1964年生,博士研究生.
基金项目:国家自然科学基金(1963040)、江苏省自然科学基金(BK99002)资助项目.
更新日期/Last Update: 2001-03-20