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(hào) O212.2文獻(xiàn)標(biāo)識(shí)碼 A文章編號(hào) 1000-2537（2017）06-0071-05

摘 要 在Ⅱ型刪失數(shù)據(jù)下，討論了Lindley分布參數(shù)的最大似然估計(jì).給出了參數(shù)的區(qū)間估計(jì)和逆矩估計(jì)，運(yùn)用隨機(jī)模擬的方法對(duì)參數(shù)進(jìn)行了統(tǒng)計(jì)分析.通過一個(gè)例子求出了在不同Ⅱ型刪失樣本下參數(shù)的兩種點(diǎn)估計(jì)及區(qū)間估計(jì)，并進(jìn)行了比較.

關(guān)鍵詞 Lindley分布； χ2分布；區(qū)間估計(jì)；逆矩估計(jì)；最大似然估計(jì)

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：

[1] LINDLEY D. Introduction to probability and statistics from a Bayesian viewpoint， part II： inference[M]. Cambridge： Cambridge University Press， 1965.

[2] LINDLEY D. Fiducial distributions and Bayes theorem[J].J Royal Stat Soc， 1958，20（1）：102-107.

[3] GHITANY M E， ATIEH B， NADARAJAH S. Lindley distribution and its application[J]. Math Comput Simula， 2008，78（4）：493-506.

[4] GHITANY M E， ALMDK， NADARAJAH S. Zero-truncated Poisson-Lindley distribution and its application[J]. Math Comput Simula， 2008，79（3）：279-287.

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[6] 杜偉娟，彭家龍，李體政.Lindley分布參數(shù)的經(jīng)驗(yàn)Bayes檢驗(yàn)的收斂速度[J].統(tǒng)計(jì)與決策，2012，21：23-26.

[7] 范梓淼，周菊玲. NA 樣本下Lindley 分布參數(shù)的經(jīng)驗(yàn)Bayes 檢驗(yàn)[J].貴州大學(xué)學(xué)報(bào)（自然科學(xué)版），2016，34（2）：68-70.

[8] 龍 兵. Lindley分布中參數(shù)的區(qū)間估計(jì)和假設(shè)檢驗(yàn)[J].廣西民族大學(xué)學(xué)報(bào)（自然科學(xué)版），2014，20（1）：59-62.

[9] 黃文平，周經(jīng)倫，寧菊紅，等.基于競(jìng)爭(zhēng)失效數(shù)據(jù)的Lindley分布參數(shù)估計(jì)[J].系統(tǒng)工程與電子技術(shù)，2016，38（2）：464-469.

[10] LAWLESS J F. Statistical models and methods for lifetime data[M].New York： Wiley， 2003.