【摘要】：在金融風(fēng)險(xiǎn)評(píng)估、事故預(yù)測(cè)、保險(xiǎn)索賠等領(lǐng)域的研究中,極值理論已發(fā)展成為一種重要的統(tǒng)計(jì)學(xué)方法。Gumbel分布是一種常用的極值分布函數(shù),并逐漸成為了對(duì)于隨機(jī)變量極端變異性建模的重要工具。文章將二項(xiàng)分布與Gumbel分布函數(shù)復(fù)合,提出了一種新的復(fù)合極值分布函數(shù)即二項(xiàng)-Gumbel分布。重點(diǎn)介紹了極值理論以及二項(xiàng)分布與Gumbel分布復(fù)合函數(shù),運(yùn)用極大似然估計(jì)(MLE)對(duì)二項(xiàng)-Gumbel復(fù)合分布的各種參數(shù)進(jìn)行估計(jì),并通過(guò)計(jì)算機(jī)模擬得KS檢驗(yàn)統(tǒng)計(jì)量的臨界值。
[Abstract]:In the field of financial risk assessment, accident prediction, insurance claims and so on, extreme value theory has developed into an important statistical method. Gumbel distribution is a commonly used extreme value distribution function. It has gradually become an important tool for modeling extreme variability of random variables. In this paper, binomial distribution is combined with Gumbel distribution function, and a new compound extreme distribution function, binomial Gumbel distribution, is proposed. The extreme value theory and the compound function of binomial distribution and Gumbel distribution are introduced emphatically. The parameters of binomial Gumbel compound distribution are estimated by maximum likelihood estimation (MLE), and the critical values of KS test statistics are obtained by computer simulation.
【作者單位】： 蘭州財(cái)經(jīng)大學(xué)統(tǒng)計(jì)學(xué)院;中國(guó)人民大學(xué)應(yīng)用統(tǒng)計(jì)科學(xué)研究中心;中國(guó)人民大學(xué)統(tǒng)計(jì)學(xué)院;
【分類號(hào)】：O212.1
，

本文編號(hào)：2194202