本文選題：非對稱正態(tài)分布 + 廣義伽馬分布　； 參考：《西南大學(xué)》2017年碩士論文

【摘要】：本文主要研究在最優(yōu)規(guī)范常數(shù)條件下,服從非對稱正態(tài)分布和廣義伽馬分布的獨(dú)立同分布隨機(jī)變量序列的極值分布以及觀測值的鄰近最大值的漸近性質(zhì).全文主要分為兩部分:第一部分首先根據(jù)非對稱正態(tài)分布的概率密度函數(shù)推導(dǎo)出該分布的基本性質(zhì),如Mills率,尾部表達(dá)式,并判斷出該分布的極值分布類型,確定出最優(yōu)規(guī)范化常數(shù).在該規(guī)范化常數(shù)條件下,通過對尾部表達(dá)式的精確展開,得到非對稱正態(tài)分布規(guī)范化最大值的極值分布的漸近展開式及其收斂到極值分布的收斂速度.其次,根據(jù)非對稱正態(tài)分布的性質(zhì),判斷出該分布是瘦尾分布.并確定出該分布序列觀測值的鄰近最大值和鄰近最大值部分和弱收斂于指數(shù)分布的最優(yōu)規(guī)范常數(shù).第二部分首先在冪賦范條件下得到廣義伽馬分布的極值分布收斂的漸近展開式以及該分布的極值分布收斂到對應(yīng)極值分布的收斂速度.其次,根據(jù)廣義伽馬分布的性質(zhì),判斷出該分布是瘦尾分布.并確定該分布序列觀測值的鄰近最大值和鄰近最大值部分和弱收斂于指數(shù)分布的最優(yōu)規(guī)范常數(shù).
[Abstract]:In this paper, under the condition of optimal gauge constant, we study the asymptotic properties of the extreme distribution of the sequence of independent identical variables of asymmetric normal distribution and generalized gamma distribution, as well as the asymptotic properties of the adjacent maximum values of the observed values. The paper is divided into two parts: in the first part, the basic properties of the asymmetric normal distribution, such as the Mills rate, the tail expression, and the extreme distribution type of the distribution are derived according to the probability density function of the asymmetric normal distribution. The optimal normalization constant is determined. Under the condition of the canonical constant, the asymptotic expansion of the extreme distribution of the normalized maximum value of the asymmetric normal distribution and the convergence rate of its convergence to the extreme value distribution are obtained by the exact expansion of the tail expression. Secondly, according to the properties of asymmetric normal distribution, it is determined that the distribution is a thin tail distribution. The adjacent maximum value and adjacent maximum partial sum of the observed values of the distribution sequence are determined, and the optimal gauge constants converging weakly to the exponential distribution are obtained. In the second part, the asymptotic expansion of the convergence of the extreme value distribution of the generalized gamma distribution and the convergence rate of the extreme value distribution of the generalized gamma distribution to the corresponding extreme value distribution are obtained under the condition of power normed. Secondly, according to the properties of the generalized gamma distribution, it is determined that the distribution is a thin tail distribution. The adjacent maximum value and adjacent maximum partial sum of the observed values of the distribution sequence are determined and the optimal gauge constants converge weakly to the exponential distribution.
【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(hào)】：F224

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相關(guān)碩士學(xué)位論文 前3條

1 杜玲玲;廣義伽馬分布及對數(shù)廣義誤差分布序列極值的漸近性質(zhì)[D];西南大學(xué);2016年

2 朱祖銳;非對稱正態(tài)分布及廣義伽馬分布序列極值的極限性質(zhì)[D];西南大學(xué);2017年

3 潘立先;四參數(shù)廣義伽馬分布函數(shù)擬合居民收入分布[D];西南財(cái)經(jīng)大學(xué);2014年

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本文編號(hào)：1993422