本文關(guān)鍵詞： 混合偏t分布 極值分布 高階展開式 線性賦范 冪賦范　出處：《西南大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

【摘要】：本文將研究在線性賦范和冪賦范兩種賦范定義下混合偏t分布極值的漸近性質(zhì)及數(shù)值模擬,全文主要分為以下三個部分.第一部分研究在線性賦范和冪賦范兩種條件下,混合偏t分布規(guī)范化最大值的分布函數(shù)的高階漸近展開式.首先,應(yīng)用偏t分布的尾部表達式可以得到混合偏t分布的尾部表達式,應(yīng)用該尾部表達式可以判斷出在線性賦范條件下混合偏t分布的極值分布類型,并且確定相應(yīng)的最優(yōu)規(guī)范化常數(shù).其次,在該最優(yōu)規(guī)范化常數(shù)條件下,通過對混合偏t分布尾部表達式的精確展開,得到在線性賦范條件下混合偏t分布規(guī)范化最大值的分布函數(shù)的高階漸近展開式.最后,通過簡單變形,得到在冪賦范條件下混合偏t分布規(guī)范化最大值的分布函數(shù)的高階漸近展開式.第二部分研究在線性賦范和冪賦范兩種條件下,混合偏t分布規(guī)范化最大值的密度函數(shù)的高階漸近展開式.首先,應(yīng)用偏t分布的密度函數(shù)的表達式得到混合偏t分布的密度函數(shù)的表達式.其次,分別利用第一部分得到的在線性賦范和冪賦范兩種條件下規(guī)范化最大值的分布函數(shù)的高階漸近展式以及混合偏t分布的密度函數(shù)的表達式,即可求得兩種賦范條件下規(guī)范化最大值的密度函數(shù)的高階漸近展開式.第三部分基于第一、二部分的結(jié)果進行數(shù)值模擬和比較.通過兩個例子分別對規(guī)范化最大值的分布函數(shù)和密度函數(shù)的各階漸近展式進行模擬,與相應(yīng)的精確值進行比較,最后用圖表的方式展示出來,進而更直觀地反映線性賦范和冪賦范兩種條件下高階漸近展式擬合精度的差異.
[Abstract]:In this paper, the asymptotic properties and numerical simulation of the extreme value of mixed partial t distribution under the definitions of linear normed and power normed are studied. In the first part, we study the higher order asymptotic expansion of the distribution function of the normalized maximum value of the mixed partial t distribution under the condition of linear normed and power normed. The tail expression of mixed partial t distribution can be obtained by using the tail expression of partial t distribution, and the extreme distribution type of mixed partial t distribution can be determined under linear normed condition. And the corresponding optimal normalization constant is determined. Secondly, under the condition of the optimal normalization constant, the exact expansion of the tail expression of the mixed partial t distribution is carried out. The higher order asymptotic expansion of the distribution function of the normalized maximum value of the mixed partial t distribution under the condition of linear normed is obtained. Finally, the simple deformation is obtained. The higher order asymptotic expansions of the distribution function of the normalized maximum value of the mixed partial t distribution under the condition of power normed are obtained. In the second part, under the condition of linear normed and power normed, the higher order asymptotic expansions of the distribution function are obtained. The higher order asymptotic expansion of the density function of the normalized maximum value of the mixed partial t distribution. Firstly, the expression of the density function of the mixed partial t distribution is obtained by using the expression of the density function of the partial partial t distribution. Secondly, the expression of the density function of the mixed partial t distribution is obtained. In the first part, the higher order asymptotic expansion of the distribution function of the normalized maximum value and the density function of the mixed partial t distribution are obtained under the condition of linear normed and power normed respectively. The higher order asymptotic expansion of the density function of the normalized maximum value under two normed conditions can be obtained. The third part is based on the first part. Through two examples, the distribution function of normalized maximum value and the asymptotic expansion of density function are simulated and compared with the corresponding exact values. Finally, it is shown in the form of graphs, and the difference of fitting accuracy of higher order asymptotic expansion under linear normed and power normed conditions is more intuitively reflected.
【學(xué)位授予單位】：西南大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：F224

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本文編號：1450361