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本文研究了一个不完全检查模型,在这种模型中只能以概率β发现试样失效,所有的试样的寿命都是相互独立并服从同一参数为λ的指数分布。当1-β较小时,利用近似似然筛选法,获得一个首阶二项自回归模型。当λ已知时,对于检验的假设β=1、而备选假设β<1提出一个局部最有效的检验,在原假设以及备选假设下,得到检验统计量的渐近分布。为了处理λ未知的情况要修改检验统计量,本文也给出它的渐近分布。最后用模拟的方法来研究由近似似然函数得到的β和λ的极大似然估计的有偏性。
In this paper, we study an incomplete inspection model, in which the failure of the specimen can only be found with the probability β, and the lifetimes of all the specimens are independent of each other and obey the exponential distribution with the same parameter λ. When 1-β is small, a first-order binomial autoregressive model is obtained by using approximate likelihood screening method. When λ is known, β = 1 for the test hypothesis, and the alternative hypothesis β <1 proposes a locally most valid test, obtaining the asymptotic distribution of the test statistic under the null hypothesis and the alternative hypothesis. In order to deal with the case of λ unknown to modify the test statistics, this paper also gives its asymptotic distribution. Finally, a simulation method is used to study the biased maximum likelihood estimation of β and λ obtained from the approximate likelihood function.