# [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] 点击复制 基于Ⅱ型截尾样本下Rayleigh分布参数的条件置信限() 分享到： var jiathis_config = { data_track_clickback: true };

31

2001年第2期

117-122

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

Author(s):
Department of Applied Mathematics,Southeast University, Nanjing 210096)

Keywords:

O212.2
DOI:
10.3969/j.issn.1001-0505.2001.02.028

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:

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