【摘要】：Generalized Birnbaum-Saunders(GBS)分布是一種較為靈活的壽命模型,該模型在產(chǎn)品的可靠性分析中應(yīng)用廣泛,且擬合效果較優(yōu),因此探究此分布的性質(zhì),統(tǒng)計(jì)推斷以及參數(shù)估計(jì)方法,成為具有理論價(jià)值和現(xiàn)實(shí)意義的課題。本文主要研究BS-Laplace(LBS)疲勞壽命分布。首先簡單介紹了LBS分布的產(chǎn)生背景,對該分布的期望、方差、變異系數(shù)、相關(guān)系數(shù)、偏度、峰度等性質(zhì)做了詳細(xì)地推導(dǎo)計(jì)算,并分析了變量X-1和Xa(a0)的分布。然后,對密度函數(shù)、失效率函數(shù)及平均失效率函數(shù)的圖像進(jìn)行了研究,證明了它們的形狀走勢,并畫出其在不同參數(shù)取值下的圖像。得出該分布密度函數(shù),失效率函數(shù)和平均失效率函數(shù)的形狀均有兩種:“倒浴盆形”和“倒浴盆-浴盆-倒浴盆形”。接著,給出了LBS分布中參數(shù)αβ,的幾種估計(jì)方法,包括矩估計(jì)1、矩估計(jì)2、逆矩估計(jì)和分位數(shù)估計(jì),并對以上幾種估計(jì)方法做了綜合比較,得出:四種方法下分位數(shù)估計(jì)對參數(shù)β的估計(jì)效果最好;矩估計(jì)2對參數(shù)α的估計(jì)效果最好;綜合比較來說,分位數(shù)估計(jì)效果較好。其次,對LBS分布中的尺度參數(shù)β做了全樣本下的區(qū)間估計(jì),并對該區(qū)間估計(jì)進(jìn)行了Monte Carlo模擬研究,結(jié)果表明該估計(jì)方法不太理想。再次,本文對LBS分布做了推廣,引入位置參數(shù)μ,提出了三參數(shù)LBSIbam),,(疲勞壽命分布,并給出了參數(shù)的矩估計(jì)和分位數(shù)估計(jì)。此外,文中在給出LBSI分布參數(shù)真值情況下,模擬得出了兩種方法下參數(shù)的估計(jì)值。
[Abstract]:The Generalized Birnbaum-Saunders (GBS) distribution is a flexible life model, which is widely used in the reliability analysis of products, and the fitting effect is better. Therefore, the properties of the distribution, statistical inference and parameter estimation methods are explored. It has become a topic of theoretical value and practical significance. The distribution of fatigue life of BS-Laplace (LBS) is studied in this paper. In this paper, the background of LBS distribution is introduced briefly. The properties of the distribution, such as expectation, variance, coefficient of variation, correlation coefficient, bias and kurtosis, are deduced and calculated in detail, and the distributions of variables X-1 and Xa (a0) are analyzed. Then, the images of density function, failure rate function and average failure rate function are studied, their shape trend is proved, and the images with different parameters are drawn. The distribution density function, the failure rate function and the average failure rate function have two shapes: "inverted bathtub shape" and "inverted bathtub-inverted bathtub shape". Then, several estimation methods of parameter 偽 尾 in LBS distribution are given, including moment estimation 1, moment estimation 2, inverse moment estimation and quantile estimation. It is concluded that quantile estimation is the best method for parameter 尾 estimation. Moment estimation 2 has the best effect on parameter 偽, and the quantile estimation is better than other methods. Secondly, the interval estimation of the scale parameter 尾 in the LBS distribution is made under the whole sample, and the Monte Carlo simulation of the interval estimation is carried out. The results show that the estimation method is not very satisfactory. Thirdly, we generalize the LBS distribution, introduce the position parameter 渭, propose the three-parameter LBSIbam), (fatigue life distribution, and give the moment estimation and quantile estimation of the parameters. In addition, when the true values of LBSI distribution parameters are given, the estimated values of the two methods are obtained by simulation.
【學(xué)位授予單位】：上海師范大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O213.2

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