Ⅱ型刪失下Lindley分布的參數估計（英文）

龍兵

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

中圖分類號 O212.2文獻標識碼 A文章編號 1000-2537（2017）06-0071-05

摘 要 在Ⅱ型刪失數據下，討論了Lindley分布參數的最大似然估計.給出了參數的區間估計和逆矩估計，運用隨機模擬的方法對參數進行了統計分析.通過一個例子求出了在不同Ⅱ型刪失樣本下參數的兩種點估計及區間估計，并進行了比較.

關鍵詞 Lindley分布； χ2分布；區間估計；逆矩估計；最大似然估計

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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[8] 龍 兵. Lindley分布中參數的區間估計和假設檢驗[J].廣西民族大學學報（自然科學版），2014，20（1）：59-62.

[9] 黃文平，周經倫，寧菊紅，等.基于競爭失效數據的Lindley分布參數估計[J].系統工程與電子技術，2016，38（2）：464-469.

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