Selecting the optimal sample fraction in univariate extreme value estimation

high volatility, thick tails and extreme value theory in value at risk estimation: the case of liability insurance in iran insurance company

در این بررسی ابتدا به بررسی ماهیت توزیع خسارات پرداخته میشود و از روش نظریه مقادیر نهایی برای بدست آوردن برآورد ارزش در معرض خطر برای خسارات روزانه بیمه مسئولیت شرکت بیمه ایران استفاده میشود. سپس کارایی نظریه مقدار نهایی در برآورد ارزش در معرض خطر با کارایی سایر روشهای واریانس ، کواریانس و روش شبیه سازی تاریخی مورد مقایسه قرار میگیرد. نتایج این بررسی نشان میدهند که توزیع ،garch شناخته شده مدل...

On Univariate Extreme Value Statistics and the Estimation of Reinsurance Premiums

Overview (Re)insurance premium calculation Net premium principle Wang's premium principle applied to excess-of-loss reinsurance setting Extreme value statistics Motivation Extreme value theory (first order framework) Estimating reinsurance premiums Finite sample behavior Simulated data (Fréchet, Burr) Reinsurance premiums (net premium, dual-power transform) X non-negative random variable denoti...

Selecting the Smallest Extreme Value Population with the Smallest Variance

Finite sample inference for extreme value distributions

We consider the problem of small sample inference for the generalised extreme value distribution. In particular, we show the existence of approximate and exact ancillary statistics for this distribution and that small sample likelihood based inference is greatly improved by conditioning on these statistics. Ignoring the ancillary statistics in inference can have severe consequences in some stan...

Estimation for the Type-II Extreme Value Distribution Based on Progressive Type-II Censoring

In this paper, we discuss the statistical inference on the unknown parameters and reliability function of type-II extreme value (EVII) distribution when the observed data are progressively type-II censored. By applying EM algorithm, we obtain maximum likelihood estimates (MLEs). We also suggest approximate maximum likelihood estimators (AMLEs), which have explicit expressions. We provide Bayes ...