Bayesian approach for optimal PV system sizing under climate change

This paper proposes a novel statistical approach for optimally sizing a stand-alone photovoltaic (PV) system under climate change. Traditionally, the irradiation profile of a typical day or year is used to size PV systems. However, facing the global warming crisis as well as the fact that no two years would have the same weather condition for a single site, this often makes the traditional way failed in the extreme weather conditions. This paper presents a method to statistically model the trend of climate change year by year and put it into the sizing formula, so that the results are optimal for the current weather condition and confidential for the future as well. Hence, the suitable sizes for the PV array and the number of batteries are obtained by pure computation. This is different from the traditional simulation-based sizing curve method. An economic optimization procedure is also presented. In addition to the capital and maintenance costs, a penalty cost is introduced when service fails. A new statistic-based reliability index, the loss of power probability, in terms of threshold-based Extreme Value Theory is presented. This index indicates the upper bound reliability for applications and provides rich information for many extreme events. A technological and economic comparison among the traditional daily energy balance method, sizing curve method and the proposed approach is conducted to demonstrate the usefulness of the new method.     

On the mean residual life of records

Suppose that a technical system is subject to shocks, e.g. peaks of voltages from a sequence of identically independent voltages having a lower limit value v>0$v>0$. We propose a new definition for the mean residual life of the records of the sequence and study its various properties.     

Risks of Mortality and Morbidity from Worldwide Terrorism: 1968–2004

Worldwide data on terrorist incidents between 1968 and 2004 gathered by the RAND Corporation and the Oklahoma City National Memorial Institute for the Prevention of Terrorism (MIPT) were assessed for patterns and trends in morbidity/mortality. Adjusted data analyzed involve a total of 19,828 events, 7,401 "adverse" events (each causing >or= 1 victim), and 86,568 "casualties" (injuries), of which 25,408 were fatal. Most terror-related adverse events, casualties, and deaths involved bombs and guns. Weapon-specific patterns and terror-related risk levels in Israel (IS) have differed markedly from those of all other regions combined (OR). IS had a fatal fraction of casualties about half that of OR, but has experienced relatively constant lifetime terror-related casualty risks on the order of 0.5%--a level 2 to 3 orders of magnitude more than those experienced in OR that increased approximately 100-fold over the same period. Individual event fatality has increased steadily, the median increasing from 14% to 50%. Lorenz curves obtained indicate substantial dispersion among victim/event rates: about half of all victims were caused by the top 2.5% (or 10%) of harm-ranked events in OR (or IS). Extreme values of victim/event rates were approximated fairly well by generalized Pareto models (typically used to fit to data on forest fires, sea levels, earthquakes, etc.). These results were in turn used to forecast maximum OR- and IS-specific victims/event rates through 2080, illustrating empirically-based methods that could be applied to improve strategies to assess, prevent, and manage terror-related risks and consequences.     

金融发展优先于金融改革——一个基于中国现状的金融效率改进分析

相对于我国金融效率改进研究的主流认识,该文论述了另一种可能的路径选择,即“金融产业发展”的路径选择。文章通过金融配置效率决定因素的原始模型分析,认为在影响金融效率实现的两个基本市场条件中,市场完全性(completeness)是制约金融效率的直接市场条件,而市场完备性(perfection)是一般性的市场条件。因此,一个经济的金融效率改进过程应遵循“市场完全性先于市场完备性”的原则。作者主张我国金融效率的帕累托改进过程应是：金融产业市场结构化→权证资产（工具）丰富化→权证市场规模扩大化。     

Opportunities of the minimum Anderson–Darling estimator as a variant of the maximum likelihood method

We reveal that the minimum Anderson–Darling (MAD) estimator is a variant of the maximum likelihood method. Furthermore, it is shown that the MAD estimator offers excellent opportunities for parameter estimation if there is no explicit formulation for the distribution model. The computation time for the MAD estimator with approximated cumulative distribution function is much shorter than that of the classical maximum likelihood method with approximated probability density function. Additionally, we research the performance of the MAD estimator for the generalized Pareto distribution and demonstrate a further advantage of the MAD estimator with an issue of seismic hazard analysis.     

Inferences on functions of Pareto parameters with application to income inequality measures

The Theil, Pietra, Éltetö and Frigyes measures of income inequality associated with the Pareto distribution function are expressed in terms of parameters defining the Pareto distribution. Inference procedures based on the generalized variable method, the large sample method, and the Bayesian method for testing of, and constructing confidence interval for, these measures are discussed. The results of Monte Carlo study are used to compare the performance of the suggested inference procedures from a population characterized by a Pareto distribution.     

On optimising the estimation of high quantiles of a probability distribution

One of the major aims of one-dimensional extreme-value theory is to estimate quantiles outside the sample or at the boundary of the sample. The underlying idea of any method to do this is to estimate a quantile well inside the sample but near the boundary and then to shift it somehow to the right place. The choice of this “anchor quantile” plays a major role in the accuracy of the method. We present a bootstrap method to achieve the optimal choice of sample fraction in the estimation of either high quantile or endpoint estimation which extends earlier results by Hall and Weissman (1997) in the case of high quantile estimation. We give detailed results for the estimators used by Dekkers et al. (1989). An alternative way of attacking problems like this one is given in a paper by Drees and Kaufmann (1998).     

z Test for the significance of the mean of a stable probability distribution with 1<α≤2

The analysis of data using a stable probability distribution with tail parameter α<2 (sometimes called a Pareto–Levy distribution) seems to have been avoided in the past in part because of the lack of a significance test for the mean, even though it appears to be the correct distribution to use for describing returns in the financial markets. A z test for the significance of the mean of a stable distribution with tail parameter 1<α≤2 is defined. Tables are calculated and displayed for the 5% and 1% significance levels for a range of tail and skew parameters α and β. Through the use of maximum likelihood estimates, the test becomes a practical tool even when α and β are not that accurately determined. As an example, the z test is applied to the daily closing prices for the Dow Jones Industrial average from 2 January 1940 to 19 March 2010.     

The Extremal Dependence Measure and Asymptotic Independence

Abstract

Extremal dependence analysis assesses the tendency of large values of components of a random vector to occur simultaneously. This kind of dependence information can be qualitatively different than what is given by correlation which averages over the total body of the joint distribution. Also, correlation may be completely inappropriate for heavy tailed data. We study the extremal dependence measure (EDM), a measure of the tendency of large values of components of a random vector to occur simultaneously and show consistency of an estimator of the EDM. We also show asymptotic normality of an idealized estimator in a restricted case of multivariate regular variation where scaling functions do not have to be estimated.     

Extended generalised Pareto models for tail estimation

The most popular approach in extreme value statistics is the modelling of threshold exceedances using the asymptotically motivated generalised Pareto distribution. This approach involves the selection of a high threshold above which the model fits the data well. Sometimes, few observations of a measurement process might be recorded in applications and so selecting a high quantile of the sample as the threshold leads to almost no exceedances. In this paper we propose extensions of the generalised Pareto distribution that incorporate an additional shape parameter while keeping the tail behaviour unaffected. The inclusion of this parameter offers additional structure for the main body of the distribution, improves the stability of the modified scale, tail index and return level estimates to threshold choice and allows a lower threshold to be selected. We illustrate the benefits of the proposed models with a simulation study and two case studies.