本文選題：概率分布　切入點(diǎn)：約束選擇　出處：《西南交通大學(xué)》2017年碩士論文

【摘要】：概率密度函數(shù)包含了隨機(jī)變量幾乎所有的信息,根據(jù)已經(jīng)得到的樣本數(shù)據(jù)去估計(jì)隨機(jī)變量的概率密度函數(shù),即概率密度函數(shù)估計(jì),它是概率與數(shù)理統(tǒng)計(jì)中的一個(gè)基本問題。與此同時(shí),在許多與實(shí)際問題相關(guān)的應(yīng)用研究當(dāng)中,也都以此為基礎(chǔ),從而開展對(duì)本領(lǐng)域知識(shí)及問題的研究和探討。由此可見,概率密度函數(shù)估計(jì)在理論研究以及實(shí)際的工程應(yīng)用中都扮演著十分重要的角色。按照傳統(tǒng)對(duì)概率密度函數(shù)估計(jì)方法的分類標(biāo)準(zhǔn),可將這一問題的研究分為以下三類:參數(shù)化方法、非參方法以及半?yún)⒎椒�。由于在大多�?shù)與現(xiàn)實(shí)問題相關(guān)的應(yīng)用研究當(dāng)中,對(duì)于概率密度函數(shù)的具體模型所對(duì)應(yīng)的信息往往無從得知,因此,類似這類問題的求解通常不大會(huì)使用參數(shù)化方法和半?yún)⒎椒āＵ腔谶@樣的考慮,使得非參方法成為人們?cè)谘芯扛怕拭芏群瘮?shù)估計(jì)問題時(shí)應(yīng)用最為普遍的一種方法。而在非參方法中,由于核方法最終能給到概率密度函數(shù)的具體的顯示解,因而被人們廣泛地研究和使用。盡管如此,對(duì)概率密度函數(shù)使用核方法進(jìn)行估計(jì)時(shí),依然存在核函數(shù)及窗口寬度較難確定的缺點(diǎn)�；诖�,本文在較深入理解最大熵原理的情況下,針對(duì)其如何對(duì)常見分布開展參數(shù)估計(jì)進(jìn)行了較詳細(xì)論述,并總結(jié)出了基于最大熵原理對(duì)常見分布開展參數(shù)估計(jì)的一般步驟。最大熵方法的思想大致如下:在給定某些約束條件的情形下,從符合這些約束的分布當(dāng)中,選擇熵值最大的分布作為理想的分布才是合情合理的。而針對(duì)實(shí)際問題而言,要想使得所推導(dǎo)出來的分布與所要研究的系統(tǒng)的已知信息相一致,找出確定分布的約束便成了使用最大熵原理估計(jì)概率密度函數(shù)的關(guān)鍵。也正是基于這樣的考慮,本文提出了一種有效的選擇約束條件的方法,在此基礎(chǔ)上利用最大熵原理對(duì)概率密度函數(shù)進(jìn)行估計(jì)。通過仿真數(shù)據(jù)表明,該方法能較合理地選擇出數(shù)據(jù)服從真實(shí)分布下基于最大熵原理所需要滿足的約束,并得出結(jié)論:基于本文提出的選擇約束的方法利用最大熵原理去估計(jì)概率密度函數(shù)確實(shí)是一種無論從理論還是從實(shí)現(xiàn)上來講都是較為容易、且行之有效的方法。
[Abstract]:The probability density function contains almost all the information of random variables. It is a basic problem in probability and mathematical statistics to estimate the probability density function of random variables according to the obtained sample data.At the same time, in many practical problems related to the application of research, also on the basis of this, so as to carry out the field of knowledge and problems of research and discussion.Thus, probability density function estimation plays an important role in both theoretical research and practical engineering applications.According to the traditional classification criteria of probability density function estimation, the research on this problem can be divided into the following three categories: parameterization method, non-parametric method and semi-parametric method.Because the information of the specific model of probability density function is often unknown in most practical application studies, parameterized methods and semi-parametric methods are not usually used to solve such problems.Because of this consideration, nonparametric method has become the most popular method in the study of probability density function estimation.In the nonparametric method, the kernel method is widely studied and used because it can finally give the concrete explicit solution of the probability density function.However, when the probability density function is estimated by kernel method, the kernel function and the width of the window are still difficult to determine.Based on this, this paper discusses in detail how to carry out parameter estimation of common distribution, and summarizes the general steps of parameter estimation for common distribution based on maximum entropy principle.The idea of the maximum entropy method is as follows: it is reasonable to choose the distribution with the largest entropy value as the ideal distribution from the distribution according to these constraints given some constraint conditions.In order to make the distribution consistent with the known information of the system, finding out the constraints of the distribution is the key to estimate the probability density function using the maximum entropy principle.Based on this consideration, this paper proposes an effective method to select constraint conditions, and then estimates the probability density function by using the maximum entropy principle.The simulation data show that the method can reasonably select the constraints that must be satisfied by the principle of maximum entropy in the real distribution.It is concluded that the method of choosing constraints proposed in this paper to estimate the probability density function by using the maximum entropy principle is an easy and effective method both theoretically and practically.
【學(xué)位授予單位】：西南交通大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O212.1

【參考文獻(xiàn)】

相關(guān)期刊論文 前2條

1 張立振;徐德倫;;A New Maximum Entropy Probability Function for the Surface Elevation of Nonlinear Sea Waves[J];China Ocean Engineering;2005年04期

2 俞禮軍,嚴(yán)海,嚴(yán)寶杰;最大熵原理在交通流統(tǒng)計(jì)分布模型中的應(yīng)用[J];交通運(yùn)輸工程學(xué)報(bào);2001年03期

相關(guān)博士學(xué)位論文 前1條

1 陶山山;多維最大熵模型及其在海岸和海洋工程中的應(yīng)用研究[D];中國海洋大學(xué);2013年

相關(guān)碩士學(xué)位論文 前1條

1 李憲東;基于最大熵原理的確定概率分布的方法研究[D];華北電力大學(xué)（北京）;2008年

，

本文編號(hào)：1715786