Ⅱ型删失下Lindley分布的参数估计（英文）

龙兵

Abstract Maximum likelihood estimation of the parameter from the Lindley distribution was discussed under Ⅱ censored data. The interval estimation and inverse moment estimation were given， and the random simulation method was used to analyze the parameter. An example was provided to find out the two kinds of point estimation and interval estimation about the parameter under different type Ⅱ censored samples.Comparison between the two point estimations was discussed.

Key words Lindley distribution； Chi-quare distribution； interval estimation； inverse moment estimation； maximum likelihood estimation

中圖分类号 O212.2文献标识码 A文章编号 1000-2537（2017）06-0071-05

摘 要 在Ⅱ型删失数据下，讨论了Lindley分布参数的最大似然估计.给出了参数的区间估计和逆矩估计，运用随机模拟的方法对参数进行了统计分析.通过一个例子求出了在不同Ⅱ型删失样本下参数的两种点估计及区间估计，并进行了比较.

关键词 Lindley分布； χ2分布；区间估计；逆矩估计；最大似然估计

Lindley distribution was proposed by Lindley in the literature[1-2] in 1958， which is an important distribution in reliability study. For some life data， the use of Lindley distribution model to fit the effect will be better. At present， there are a lot of statistical scholars who have discussed its properties， and obtained a lot of research results. The properties and applications of compound Lindley distribution were studied in the literatures [3-5]. The empirical Bayes one-sided test was discussed in the literature [6] in the case of independent identically distributed sample. The EB test function was constructed by using the recursive kernel estimation of density function. The optimality of the test function was proved， and the convergence rate was obtained. The empirical Bayes test function of the parameter from Lindley distribution was discussed based on NA random sample sequence in the literature [7]. The interval estimation and hypothesis testing of the parameter in Lindley distribution were studied in the full sample in the literature [8]. The failure model of incomplete data with Lindley distribution was discussed in the literature[9]，and maximum likelihood estimation method was used to obtain point estimation and asymptotic confidence interval estimation of the model. An example was given to show that the Lindley distribution have better adaptability compared with exponential distribution and Weibull distribution.

In this paper， we will discuss the maximum likelihood estimation， interval estimation and inverse moment estimation of the parameter from Lindley distribution in Ⅱ censored samples， the parameter will be estimated by the method of stochastic simulation， and the average deviation will be calculated. Finally， an example will be given to illustrate the feasibility of the proposed method.

References：

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[7] 范梓淼，周菊玲. NA 样本下Lindley 分布参数的经验Bayes 检验[J].贵州大学学报（自然科学版），2016，34（2）：68-70.

[8] 龙 兵. Lindley分布中参数的区间估计和假设检验[J].广西民族大学学报（自然科学版），2014，20（1）：59-62.

[9] 黄文平，周经伦，宁菊红，等.基于竞争失效数据的Lindley分布参数估计[J].系统工程与电子技术，2016，38（2）：464-469.

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