Simulation of certain multivariate generalized Pareto distributions

The investigation of multivariate generalized Pareto distributions (GPDs) has begun only recently. For further progress with these distributions simulation methods are an important part. We describe several methods of simulating GPDs, beginning with an efficient method for the logistic GPD. The algorithm is based on the Shi transformation, which was already used for the simulation of multivariate extreme value distributions (EVDs) of logistic type. In the sequel another algorithm is presented simulating a broader class of GPDs. Due to its numerical complexity it is only practicably applicable in low dimensions. A method is given to generate unconditional GPD random vectors from conditionally GPD distributed random vectors. A short application of the simulation methods in the analysis of a real hydrological data set concludes the article. The simulation algorithms are available on the author’s home page .      

青霉素类药物的红外光谱鉴别

利用傅里叶变换红外光谱法直接测定了 5种常见的青霉素药物 ,结果表明 ,各种青霉素药物由于其化学成分及其含量不同 ,显示出独特的红外光谱图 ,但青霉素药物共同的结构特征具有相似的红外光谱特征吸收峰。该方法具有快速、准确、制样简单 ,不需进行提取分离、保持其原性质等特点     

A discussion on mean excess plots

The mean excess plot is a tool widely used in the study of risk, insurance and extreme values. One use is in validating a generalized Pareto model for the excess distribution. This paper investigates some theoretical and practical aspects of the use of the mean excess plot.     

Counting humps and peaks in generalized Motzkin paths

Let us call a lattice path in $\mathbb{Z}\times \mathbb{Z}$ from $(0,0)$ to $(n,0)$ using $U=(1,k)$, $D=(1,?1)$, and $H=(a,0)$ steps and never going below the $x$-axis, a $(k,a)$-path (of order $n$). A super   $(k,a)$-path is a $(k,a)$-path which is permitted to go below the $x$-axis. We relate the total number of humps in all of the $(k,a)$-paths of order $n$ to the number of super $(k,a)$-paths, where a hump is defined to be a sequence of steps of the form $U{H}^{i}D$, $i\ge 0$. This generalizes recent results concerning the cases when $k=1$ and $a=1$ or $a=\infty$. A similar relation may be given involving peaks (consecutive steps of the form $UD$).     

Univariate and bivariate GPD methods for predicting extreme wind storm losses

Wind storm and hurricane risks are attracting increased attention as a result of recent catastrophic events. The aim of this paper is to select, tailor, and develop extreme value methods for use in wind storm insurance. The methods are applied to the 1982-2005 losses for the largest Swedish insurance company, the Länsförsäkringar group. Both a univariate and a new bivariate Generalized Pareto Distribution (GPD) gave models which fitted the data well. The bivariate model led to lower estimates of risk, except for extreme cases, but taking statistical uncertainty into account the two models lead to qualitatively similar results. We believe that the bivariate model provided the most realistic picture of the real uncertainties. It additionally made it possible to explore the effects of changes in the insurance portfolio, and showed that loss distributions are rather insensitive to portfolio changes. We found a small trend in the sizes of small individual claims, but no other trends. Finally, we believe that companies should develop systematic ways of thinking about “not yet seen” disasters.     

NMR and HPLC study of chiral selectors with naphthyl unit

Doubling of resonances in NMR spectra of chiral selectors with naphthyl group attached to the tertiary amide nitrogen atom has been noticed what revealed the presence of two isomers. To test the enantiorecognition ability of these chiral selectors they are covalently bonded to the HPLC silica gel. Those kind of chiral stationary phases were compared with analogous commercial leucine chiral stationary phase. They exhibit the better enantioseparation results which indicate that the existence of cis/trans isomers does not have the negative influence on their enantioselective ability.

Application of Double Deposition and Stripping Steps System for Minimization of Interferences of Peaks’ Overlapping in Anodic Stripping Voltammetry

An anodic stripping voltammetric procedure for the determination of bismuth in the presence of excess of Cu²⁺ ions at two ex situ plated gold film electrodes was described. The procedure is based on utilization of two deposition and two stripping steps system. The presented procedure ensures increasing the sensitivity of Bi³⁺ determination and minimization of interferences related to peaks’ overlapping. The calibration graph for bismuth determination was linear from 2.5×10⁻⁹ to 2×10⁻⁸ mol L⁻¹ for deposition time of 300 s at both working electrodes while detection limit was 7.7×10⁻¹⁰ mol L⁻¹.