基于Ⅱ型截尾样本下Rayleigh分布参数的条件置信限

Conditional Confidence Intervals of the Parameters for Two-Parameter Rayleigh Distribution Based on Type-Ⅱ Censored Samples

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)σ e(x- μ) 2σ 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=( ^μ - μ) ^σ,Z2 =^σ σ建立在可观测的辅助统计量a =(a1 ,a2 ,… ,ar) (ai=(X(i) - ^μ) ^σ;μ ,^σ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 .

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)σ e -(x-μ) 2σ 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: Z 1=(-μ) ^σ, Z 2=/σ under the condition of the ancillary statistics: a=(a 1,a 2,…,a r) based on type Ⅱ censored sample from R(μ,σ) ,where a i=(X (i) -) ^σ,, are MLEs of μ,σ respectively. Then, we obtain conditional confidence intervals of parameters μ,σ on theobserved values of a=(a 1,a 2,…,a r). Finally, we give computational methods of conditional confidence limits of p fractile x p and tolerance interval of R(μ,σ).