No Arabic abstract
Measures of tail dependence between random variables aim to numerically quantify the degree of association between their extreme realizations. Existing tail dependence coefficients (TDCs) are based on an asymptotic analysis of relevant conditional probabilities, and do not provide a complete framework in which to compare extreme dependence between two random variables. In fact, for many important classes of bivariate distributions, these coefficients take on non-informative boundary values. We propose a new approach by first considering global measures based on the surface area of the conditional cumulative probability in copula space, normalized with respect to departures from independence and scaled by the difference between the two boundary copulas of co-monotonicity and counter-monotonicity. The measures could be approached by cumulating probability on either the lower left or upper right domain of the copula space, and offer the novel perspective of being able to differentiate asymmetric dependence with respect to direction of conditioning. The resulting TDCs produce a smoother and more refined taxonomy of tail dependence. The empirical performance of the measures is examined in a simulated data context, and illustrated through a case study examining tail dependence between stock indices.
Tail dependence refers to clustering of extreme events. In the context of financial risk management, the clustering of high-severity risks has a devastating effect on the well-being of firms and is thus of pivotal importance in risk analysis.When it comes to quantifying the extent of tail dependence, it is generally agreed that measures of tail dependence must be independent of the marginal distributions of the risks but rather solely copula-dependent. Indeed, all classical measures of tail dependence are such, but they investigate the amount of tail dependence along the main diagonal of copulas, which has often little in common with the concentration of extremes in the copulas domain of definition.In this paper we urge that the classical measures of tail dependence may underestimate the level of tail dependence in copulas. For the Gaussian copula, however, we prove that the classical measures are maximal. The implication of the result is two-fold: On the one hand, it means that in the Gaussian case, the (weak) measures of tail dependence that have been reported and used are of utmost prudence, which must be a reassuring news for practitioners. On the other hand, it further encourages substitution of the Gaussian copula with other copulas that are more tail dependent.
This article describes mathematical methods for estimating the top-tail of the wealth distribution and therefrom the share of total wealth that the richest $p$ percent hold, which is an intuitive measure of inequality. As the data base for the top-tail of the wealth distribution is inevitably less complete than the data for lower wealth, the top-tail distribution is replaced by a parametric model based on a Pareto distribution. The different methods for estimating the parameters are compared and new simulations are presented which favor the maximum-likelihood estimator for the Pareto parameter $alpha$. New criteria for the choice of other parameters are presented which have not yet been discussed in the literature before. The methods are applied to the 2012 data from the ECB Household and Consumption Survey (HFCS) for Germany and the corresponding rich list from the Manager Magazin. In addition to a presentation of all formulas, R scripts implementing them are provided by the author.
In 2017 an estimated 3 billion people used polluting fuels and technologies as their primary cooking solution, with 3.8 million deaths annually attributed to household exposure to the resulting fine particulate matter air pollution. Currently, health burdens are calculated using aggregations of fuel types, e.g. solid fuels, as country-level estimates of the use of specific fuel types, e.g. wood and charcoal, are unavailable. To expand the knowledge base about impacts of household air pollution on health, we develop and implement a Bayesian hierarchical model, based on Generalized Dirichlet Multinomial distributions, that jointly estimates non-linear trends in the use of eight key fuel types, overcoming several data-specific challenges including missing or combined fuel use values. We assess model fit using within-sample predictive analysis and an out-of-sample prediction experiment to evaluate the models forecasting performance.
Industrial and residential activities respond distinctly to electricity demand on temperature. Due to increasing temperature trend on account of global warming, its impact on peak electricity demand is a proxy for effective management of electricity infrastructure. Few studies explore the relationship between electricity demand and temperature changes in industrial areas in India mainly due to the limitation of data. The precise role of industrial and residential activities response to the temperature is not explored in sub-tropical humid climate of India. Here, we show the temperature sensitivity of industrial and residential areas in the city of Pune, Maharashtra by keeping other influencing variables on electricity demand as constant. The study seeks to estimate the behaviour of peak electricity demand with the apparent temperature (AT) using the Extreme Value Theory. Our analysis shows that industrial activities are not much influenced by the temperature whereas residential activities show around 1.5-2% change in average electricity demand with 1 degree rise in AT. Further, we show that peak electricity demand in residential areas, performed using stationary and non-stationary GEV models, are significantly influenced by the rise in temperature. The study shows that with the improvement in data collection, better planning for the future development, accounting for the climate change effects, will enhance the effectiveness of electricity distribution system. The study is limited to the geographical area of Pune. However, the methods are useful in estimating the peak power load attributed to climate change to other geographical regions located in subtropical and humid climate.
Air pollution is a major risk factor for global health, with both ambient and household air pollution contributing substantial components of the overall global disease burden. One of the key drivers of adverse health effects is fine particulate matter ambient pollution (PM$_{2.5}$) to which an estimated 3 million deaths can be attributed annually. The primary source of information for estimating exposures has been measurements from ground monitoring networks but, although coverage is increasing, there remain regions in which monitoring is limited. Ground monitoring data therefore needs to be supplemented with information from other sources, such as satellite retrievals of aerosol optical depth and chemical transport models. A hierarchical modelling approach for integrating data from multiple sources is proposed allowing spatially-varying relationships between ground measurements and other factors that estimate air quality. Set within a Bayesian framework, the resulting Data Integration Model for Air Quality (DIMAQ) is used to estimate exposures, together with associated measures of uncertainty, on a high resolution grid covering the entire world. Bayesian analysis on this scale can be computationally challenging and here approximate Bayesian inference is performed using Integrated Nested Laplace Approximations. Model selection and assessment is performed by cross-validation with the final model offering substantial increases in predictive accuracy, particularly in regions where there is sparse ground monitoring, when compared to current approaches: root mean square error (RMSE) reduced from 17.1 to 10.7, and population weighted RMSE from 23.1 to 12.1 $mu$gm$^{-3}$. Based on summaries of the posterior distributions for each grid cell, it is estimated that 92% of the worlds population reside in areas exceeding the World Health Organizations Air Quality Guidelines.