本文選題：Pareto分布　切入點(diǎn)：均勻分布　出處：《北京交通大學(xué)》2017年碩士論文　論文類(lèi)型：學(xué)位論文

【摘要】：Pareto分布和均勻分布由于其應(yīng)用廣泛一直受到研究者的重視,提出了多種參數(shù)估計(jì)方法,其中常用的有:極大似然估計(jì)、無(wú)偏估計(jì)和貝葉斯估計(jì)等等。大樣本情況下,這幾種方法都能夠獲得準(zhǔn)確的結(jié)果。而小樣本情況下,我們通常使用貝葉斯估計(jì)方法,但貝葉斯估計(jì)方法在計(jì)算參數(shù)估計(jì)時(shí),常常存在積分困難的情況,若使用Gibbs抽樣方法,運(yùn)算時(shí)計(jì)算量巨大,給參數(shù)估計(jì)帶來(lái)麻煩。在此基礎(chǔ)上,本文提出了一種新的參數(shù)估計(jì)——二次貝葉斯估計(jì)。文章中,在定義統(tǒng)計(jì)量T的基礎(chǔ)上,引入統(tǒng)計(jì)量T2,構(gòu)造出參數(shù)的二次貝葉斯估計(jì)。二次貝葉斯估計(jì)既采納了先驗(yàn)信息,同時(shí)避免了計(jì)算繁瑣的后驗(yàn)期望。文章首先通過(guò)計(jì)算獲得這兩類(lèi)分布的二次貝葉斯估計(jì)的顯式解;其次在均方誤差準(zhǔn)則下,證明了二次貝葉斯估計(jì)優(yōu)于極大似然估計(jì)與一致最小方差無(wú)偏估計(jì)。數(shù)值模擬比較發(fā)現(xiàn),無(wú)論先驗(yàn)的選擇和先驗(yàn)分布的參數(shù)取值如何變化,二次貝葉斯估計(jì)與貝葉斯估計(jì)均非常相近。隨著樣本容量n的增大,二次貝葉斯估計(jì)向貝葉斯估計(jì)趨近;同時(shí),隨著先驗(yàn)信息的集中,二次貝葉斯估計(jì)也向貝葉斯估計(jì)趨近。綜上所述,二次貝葉斯估計(jì)對(duì)Pareto分布和均勻分布都是有效的。
[Abstract]:Because of its wide application, Pareto distribution and uniform distribution have been paid much attention to by researchers. A variety of parameter estimation methods are proposed, such as maximum likelihood estimation, unbiased estimation, Bayesian estimation and so on. In the case of small sample, we usually use Bayesian estimation method, but Bayesian estimation method often has difficulty in calculating parameter estimation, if we use Gibbs sampling method, In this paper, a new parameter estimator, quadratic Bayesian estimation, is proposed. In this paper, based on the definition of statistical quantity T, a new parameter estimation is proposed. The quadratic Bayesian estimation of parameters is constructed by introducing the statistic T2. The quadratic Bayesian estimation not only adopts the prior information, At the same time, the complicated posteriori expectation is avoided. Firstly, the explicit solution of the quadratic Bayesian estimation of these two kinds of distributions is obtained by calculation; secondly, under the mean square error criterion, It is proved that the quadratic Bayesian estimation is superior to the maximum likelihood estimation and the uniform minimum variance unbiased estimation. The quadratic Bayesian estimation is very similar to the Bayesian estimation. With the increase of the sample size n, the quadratic Bayesian estimation approaches to the Bayesian estimation, at the same time, with the concentration of prior information, Quadratic Bayesian estimation also approaches to Bayesian estimation. In conclusion, quadratic Bayesian estimation is effective for both Pareto distribution and uniform distribution.
【學(xué)位授予單位】：北京交通大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O212.8

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相關(guān)期刊論文 前2條

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本文編號(hào)：1617344