【摘要】：記錄值是一種常見的數(shù)據(jù)表現(xiàn)形式,提出以來被廣泛應(yīng)用于氣象學(xué),水文學(xué),體育賽事和壽命試驗(yàn)等領(lǐng)域,例如在水文學(xué)中每年同一時(shí)期的降雨量以記錄值的形式出現(xiàn);在體育賽事中某運(yùn)動項(xiàng)目中不斷刷新新的記錄值等。記錄值是順序統(tǒng)計(jì)量的一種特殊形式。隨著對排序集抽樣研究的深入,發(fā)展起很多基于排序集抽樣的抽樣方案。結(jié)合記錄值,人們提出了一種新的排序集抽樣方法—記錄值排序集抽樣(Record RSS)。本文討論了記錄值樣本和記錄值排序集抽樣下的統(tǒng)計(jì)推斷問題,主要工作如下:(1)基于記錄值樣本,在極值分布模型下,討論了參數(shù)的點(diǎn)估計(jì)和置信區(qū)間估計(jì)問題。在點(diǎn)估計(jì)問題上,導(dǎo)出了參數(shù)的極大似然估計(jì)和逆矩估計(jì)量。在區(qū)間估計(jì)問題上,討論了參數(shù)的漸近置信區(qū)間和準(zhǔn)確置信區(qū)間;在準(zhǔn)確置信區(qū)間的建立方面,分別討論了基于2?分布和F分布的構(gòu)造方法,并討論了兩種方法下構(gòu)造的樞軸量有解的存在唯一性。最后通過一個(gè)具體實(shí)例分析討論的方法。(2)基于記錄值排序集抽樣,得到了Weibull分布參數(shù)的極大似然估計(jì),利用極大似然估計(jì)的漸進(jìn)正態(tài)性,考察了參數(shù)的漸進(jìn)置信區(qū)間,也討論了參數(shù)bootstrap法下參數(shù)的區(qū)間估計(jì)。在貝葉斯分析方面,考慮了Jeffreys和Reference先驗(yàn)作為無信息先驗(yàn)對參數(shù)進(jìn)行客觀貝葉斯統(tǒng)計(jì)推斷。由于無法直接得到參數(shù)的貝葉斯估計(jì)的數(shù)值解,利用Metropolis-Hastings算法和Gibbs抽樣解決問題。最后通過Monte-Carlo數(shù)值模擬對討論的方法進(jìn)行了對比分析。
[Abstract]:Recording value is a common form of data expression, which has been widely used in meteorology, hydrology, sports events and life testing. For example, the rainfall in the same period of each year appears in the form of recorded value in hydrology. Constantly refresh new record values in a sports event, etc. Record value is a special form of sequential statistics. With the deepening of the research on sort set sampling, many sampling schemes based on sort set sampling have been developed. Combined with record value, a new sampling method of sort set, record value sort set sampling (Record RSS)., is proposed. In this paper, the problem of statistical inference under the sampling of record value samples and record value sort sets is discussed. The main work is as follows: (1) based on the record value samples, under the extreme value distribution model, the problem of point estimation and confidence interval estimation of parameters is discussed. In the problem of point estimation, the maximum likelihood estimation and inverse moment estimation of parameters are derived. In the problem of interval estimation, the asymptotic confidence interval and accurate confidence interval of parameters are discussed, and the establishment of accurate confidence interval is discussed based on 2? The construction methods of distribution and F distribution are discussed, and the existence and uniqueness of the solution of the axis quantity constructed under the two methods are discussed. Finally, a concrete example is used to analyze and discuss the method. (2) based on the sampling of record value sort set, the maximum likelihood estimation of Weibull distribution parameters is obtained, and the progressive confidence interval of the parameters is investigated by using the asymptotic normality of maximum likelihood estimation. The interval estimation of parameters under parameter bootstrap method is also discussed. In the aspect of Bayesian analysis, Jeffreys and Reference priori are considered as non-information priori to carry out objective Bayesian statistical inference of parameters. Because the numerical solution of the parameter estimation can not be obtained directly, the Metropolis-Hastings algorithm and Gibbs sampling are used to solve the problem. Finally, the methods discussed are compared and analyzed by Monte-Carlo numerical simulation.
【學(xué)位授予單位】：成都信息工程大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O212.1

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本文編號：2496587