Extreme Value Theory

ABSTRACT We study whether option-implied conditional expectation of market loss due to tail events, or tail loss measure, contains information about future returns, especially the negative ones. Our tail loss measure predicts future market returns, magnitude, and probability of the market crashes, beyond and above other option-implied variables. Stock-specific tail loss measure predicts individual expected returns and magnitude of realized stock-specific crashes in the cross-section of stocks. An investor, especially the one who cares about the left tail of her wealth distribution (e.g., disappointment-averse), benefits from using the tail loss measure as an information variable to construct managed portfolios of a risk-free asset and market index. The tail loss measure is motivated by the results of the extreme value theory, and it is computed from observed prices of out-of-the-money put as the risk-neutral expected value of a loss beyond a given relative threshold.

Foreign portfolio investment is a major means by which emerging stock markets accumulate capital. However, the high mobility of foreign funds is a concern for local investors and policymakers in emerging countries because it may induce high stock price volatility. In this study, we utilized a riskbased approach to investigate whether the stocks most favored by foreign investors are riskier than those least favored by foreign investors. We distinguished our sample stocks into foreign most-favored and foreign least-favored groups and classified our data periods into a financial crisis period and an aftermath period. We then estimated the 1% VaRs and expected maximum losses through a GARCH– extreme value theory–copula methodology for the foreign most-favored and least-favored groups. The empirical results indicated that the foreign most-favored group had lower 1% VaRs than the foreign least-favored group during both the financial crisis and its aftermath. However, the foreign mostf...

Extrapolation techniques used for predicting long-term wind turbine loads have produced highly variable loading estimates dependent on the individual designer implementation. To reduce such variability, more precise definition and validation of these techniques are necessary. As part of a wider effort to test loads extrapolation techniques used in wind turbine design, two data sets were created. The first data set was created as an example typical of what designers use to extrapolate loads according to wind turbine design standards. The second data set was a series of year-long simulations that could be used to quantify the accuracy of extrapolation methods. Due to the large number of simulations, care was taken not to reproduce random samplings in individual time series. Additionally, a grid computing architecture was used to run the simulations in a reasonable time frame. The wind speeds where loads were highest were identified, which varied with loading type. The identification of dominant wind speeds is important to ensure an adequate number of simulations at such speeds, which often influence extrapolated loads. In-plane loads and deflections tended to be dominated by high wind speeds near cut-out wind speed. Out-ofplane loads and deflections were most influenced by winds that were near the rated wind speed. Some loads were influenced by a range of wind speeds. The loads dominated by high wind speeds had greater variability in the extreme values, which could be a reflection of the greatly varying wind and also greater sensitivity to higher energy content of the wind at such speeds.

In the past twenty years a new development in the extreme value theory has been done, especially for the "Peaks Over Threshold (POT) approach". This approach, based on the analysis of the data exceeding a sufficiently high threshold, aims to improve the efficiency of the extreme quantile estimators. The selection of an appropriate threshold is one of the important concerns of the POT approach. Various threshold selection methods, namely Square Error Method (SEM), Automated Threshold Selection Method (ATSM), and Multiple Threshold Method (MTM), has been developed. Such approaches allow avoiding subjective drawbacks of empirical and graphical methods for optimal thresholds selection. The main objective of the present study is to compare the performances of these methods in the case of financial risk estimations related to the market turmoil. The main focus of this paper is to assess the performance of the POT approach, combined to the maximum likelihood and moment methods for parameter estimations. Results show that the MTM outperforms ATSM and SEM. It is confirmed that the inverse of CAC40 return index has a Fréchet distribution tail behavior, and the parameters are better estimated by the moments method.

This study gives results of the first phase of the 12-18 year old Turkish students’ norm study of The Motivated Strategies for Learning Questionnaire (MSLQ), which deveoped by Pintrich, Smith, Garcia & McKeachie (1993). The scale was administrated to 1114 students from 3 primary schools and 3 high schools in Ankara in Turkish language, science, mathematics and social science courses. After eliminating the questionnaires which have missing and extreme values, the analyses were done on 762 valid questionnaires for motivation subscale and 1100 valid questionnaires for learning strategies subscale. Results of the confirmatory factor analyses show that the first subscale, Motivation, has six factors, and the second subscale, Learning Strategies, has nine factors according to original scale’s factor structures. Depending on the results of the confirmatory factor analysis; 6 items from motivation subscale and 5 items from learning strategies subscale were removed due to their low factor lo...

Several approximate combination formulas are currently in use for estimating the extreme values of linear combination of load eects. In this paper the focus is on one particular example of such a combination formula, viz. the so-called Turkstra's rule. Turkstra's rule was originally limited to the combination of statistically independent load eect components. It will be shown that this combination formula can be implemented in such a way that statistical dependence between the load eect components can be taken into account. This makes it possible to investigate the performance of this particular combination formula for both independent and dependent load eect components.

The main purpose of this work is to provide a broad assessment of the influence of the El Niño–southern oscillation (ENSO) on the frequency of extreme temperature events throughout the year in Argentina. The cold and warm events, defined by the persistence of significant anomalies arising from the maximum and minimum temperatures, are more intense in the subtropical latitudes, north of Argentina (northeast for cold events and northwest for warm events), during the coldest months, and in the south (higher latitudes) in the warmest months. The persistence of the air masses is always greater in the north. The warm (cold) events have a preferential region of dissipation in the northwest (northeast) of Argentina, close to the Andes. The effect of the ENSO phases on the probability of occurrences of these events has a large inter-monthly variability. The different La Niña episodes are more homogeneous in relation to their effects and feasibility for the prediction of extreme temperatures within the region, especially for cold events. During La Niña episodes, all 2 month periods (except August–September) present a higher occurrence probability of very persistent and intense cold events, compared with Neutral months in different regions of the country. Conversely, the different El Niño episodes are more heterogeneous and, therefore, their effects on temperature are more varied and so less predictable. However, El Niño episodes exhibit a stronger signal, which is associated with the tropical air incursions that generate extreme warm events, particularly in winter. These events have a higher occurrence probability in the north and a lower one in the south during the months of June to November. Cold events have a lower occurrence probability in different regions, during the El Niño phase, in the period April to September. In some cases, the ENSO signal is stronger in daily temperature values than in monthly ones over Argentina. Copyright © 2002 Royal Meteorological Society

In this paper we report directivity enhancement by a short-focal-length plano-concave lens engineered by stacked subwavelength hole arrays (fishnet-like stack) with an effective negative index of refraction close to zero, n → 0, that arises from ε and μ near-zero extreme values. The plano-concave lens frequency response shows two enhancement peaks, one at the wavelength corresponding to n = −1 and, prominent in this configuration, another unexpected peak when n → 0 that comes as a result of the similar low values of ε and μ. The frequency-dependent negative refractive index and beam-forming properties of the lens are supported by finite-integration-frequencyand time-domain simulations and experimental results. This near-zero metamaterial lens can find applications in terahertz and even optics since the building block, stacked extraordinary optical transmission layers, has already been reported for those regimes under the name of fishnet structure.

Yadav, Gilles Zumbach, and participants at the SIRIF volatility workshop (Glasgow) and the AFA meetings (New Orleans) for helpful comments. We also thank three anonymous referees and the editor for many helpful comments and suggestions that resulted in a substantial improvement of this manuscript.

Image classification in the open-world must handle out-of-distribution (OOD) images. Systems should ideally reject OOD images, or they will map atop of known classes and reduce reliability. Using open-set classifiers that can reject OOD inputs can help. However, optimal accuracy of open-set classifiers depend on the frequency of OOD data. Thus, for either standard or open-set classifiers, it is important to be able to determine when the world changes and increasing OOD inputs will result in reduced system reliability. However, during operations, we cannot directly assess accuracy as there are no labels. Thus, the reliability assessment of these classifiers must be done by human operators, made more complex because networks are not 100% accurate, so some failures are to be expected. To automate this process, herein, we formalize the open-world recognition reliability problem and propose multiple automatic reliability assessment policies to address this new problem using only the distribution of reported scores/probability data. The distributional algorithms can be applied to both classic classifiers with SoftMax as well as the open-world Extreme Value Machine (EVM) to provide automated reliability assessment. We show that all of the new algorithms significantly outperform detection using the mean of SoftMax.

Risk managers are increasingly required by international Regulatory Institutions to adopt accurate techniques for the measurement and control of portfolios financial risks. The task requires first the identification of the different risk sources affecting the portfolio and the measurement of their impact, then after: the adoption of appropriate portfolio strategies aimed at neutralising these risks. The comprehensive concept of Value-at-Risk (VaR) as a maximum tolerable loss, with a given confidence interval, has become in this regard the industry standard in risk management.

We examine the risk characteristics and capital adequacy of hedge funds through the Valueat-Risk approach. Using extensive data on nearly 1,500 hedge funds, we find only 3.7% live and 10.9% dead funds are undercapitalized as of March 2003. Moreover, the undercapitalized funds are relatively small and constitute a tiny fraction of total fund assets in our sample. Cross-sectionally, the variability in fund capitalization is related to size, investment style, age, and management fee. Hedge fund risk and capitalization also display significant time variation. Traditional risk measures like standard deviation or leverage ratios fail to detect these trends. r

In extreme excess modeling, one fits a generalized Pareto (GP) distribution to rainfall excesses above a properly selected threshold u. The latter is generally determined using various approaches, such as nonparametric methods that are intended to locate the changing point between extreme and nonextreme regions of the data, graphical methods where one studies the dependence of GP-related metrics on the threshold level u, and Goodness-of-Fit (GoF) metrics that, for a certain level of significance, locate the lowest threshold u that a GP distribution model is applicable. Here we review representative methods for GP threshold detection, discuss fundamental differences in their theoretical bases, and apply them to 1714 overcentennial daily rainfall records from the NOAA-NCDC database. We find that nonparametric methods are generally not reliable, while methods that are based on GP asymptotic properties lead to unrealistically high threshold and shape parameter estimates. The latter is justified by theoretical arguments, and it is especially the case in rainfall applications, where the shape parameter of the GP distribution is low; i.e., on the order of 0.1-0.2. Better performance is demonstrated by graphical methods and GoF metrics that rely on preasymptotic properties of the GP distribution. For daily rainfall, we find that GP threshold estimates range between 2 and 12 mm/d with a mean value of 6.5 mm/d, while the existence of quantization in the empirical records, as well as variations in their size, constitute the two most important factors that may significantly affect the accuracy of the obtained results.

Extreme returns in stock returns need to be captured for a successful risk management function to estimate unexpected loss in portfolio. Traditional value-at-risk models based on parametric models are not able to capture the extremes in emerging markets where high volatility and nonlinear behaviors in returns are observed. The Extreme Value Theory (EVT) with conditional quantile proposed by McNeil and Frey (2000) is based on the central limit theorem applied to the extremes rater than mean of the return distribution. It limits the distribution of extreme returns always has the same form without relying on the distribution of the parent variable. This paper uses 8 filtered EVT models created with conditional quantile to estimate value-at-risk for the Istanbul Stock Exchange (ISE). The performances of the filtered expected shortfall models are compared to those of GARCH, GARCH with student-t distribution, GARCH with skewed student-t distribution and FIGARCH by using alternative back-t...

Brownian motion is considered when the index y approaches the critical value 1/q. It is proved that, under a suitable (temporally inhomogeneous) normalization, it converges in law to the inverse of an extremal process which appears in the extreme value theory.

Brownian motion is considered when the index y approaches the critical value 1/q. It is proved that, under a suitable (temporally inhomogeneous) normalization, it converges in law to the inverse of an extremal process which appears in the extreme value theory.

A model for the depth-limited distribution of the highest wave in a sea state is presented. The distribution for the extreme wave height is based on a probability density function (pdf) for depth-limited wave height distribution for individual waves [Méndez, F.J., Losada, I.J., . Transformation model of wave height distribution. Coastal Eng, Vol. 50, 97:115.] and considers the correlation between consecutive waves. The model is validated using field data showing a good representation of the extreme wave heights in the surf zone. Some important statistical wave heights are parameterized obtaining useful expressions that can be used in further calculations.

This paper introduces a new class of Cox models for dependent bivariate data. The impact of the covariate on the dependence of the variables is captured through the modification of their copula. Various classes of well known copulas are stable under the model (archimedean type and extreme value copulas), meaning that the role of the covariate acts in a simple and explicit way on the copula in the class; specific parametric classes are considered.

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The large claims reinsurance treaties ECOMOR and LCR are well known not to be very popular. They have been largely neglected by most reinsurers because of their technical complexity. In this paper, we derive new mathematical results connected to asymptotic problems of these reinsurance forms. Perhaps these results can reopen the discussion on the usefulness of including the largest claims

In summer 2007, in the city of Athens, Greece, extremely high air temperatures were recorded, inducing heat discomfort conditions in the urban environment. Four biometeorological indices were calculated in order to evaluate human thermal sensation and thermal comfort: Actual Sensation Vote (ASV), Thermal Sensation-Ginovi method (TS), Discomfort Index (DI) and Heat Load Index (HL). Data included measurements of ambient temperature, temperature of the surrounding ground surface, relative humidity, air pressure, wind velocity and solar radiation obtained from National Observatory of Athens (NOA) station. During this period the daily number of patients probably affected by heat in emergency department units of cardiac clinics of four public general hospitals in Athens was recorded. The results revealed high values of DI and HL indices, demonstrating severe heat stress conditions during the last ten day period of June and July, while the ASV tends to classify too many cases into the comfort zone compared to TS, DI and HL. The statistical analysis revealed a negative relationship between the number of heat affected patients and the estimated indices values.

Autologous skin grafts are successfully used to close recalcitrant chronic wounds especially at the lower leg. If wound care is done in a dermato-plastic team approach using the bintegrated concept,Q difficulties associated with harvesting the skin graft as well as the complexities associated with inducing closure at the donor and the recipient site can be minimized. In the context of wound healing, skin transplantation can be regarded as (1) a supportive procedure for epithelialization of the wound surface and (2) mechanical stability of the wound ground. By placing skin grafts on a surface, central parts are covered much faster with keratinocytes. Skin (wound) closure is the ultimate goal, as wound closure means resistance to infection. Depending on the thickness of the skin graft, different amounts of dermis are transplanted with the overlying keratinocytes. The dermal component determines the mechanical (resistance to pressure and shear forces, graft shrinkage), functional (sensibility), and aesthetic properties of the graft. Generally speaking, the thicker the graft the better the mechanical, functional, and aesthetic properties, however, the worse the neo-and revascularization. Skin grafts do depend entirely on the re-and neovascularization coming from the wound bed. If the wound bed is seen as a recipient site for tissue graft, the classification of Lexer (Die freien Transplantationen. Stuttgart: Enke; 1924) turned out to be of extreme value. Three grades can be distinguished: bgood wound conditions,Q bmoderate wound conditions,Q and binsufficient wound conditions.Q Given good wound conditions, skin grafting is feasible. Nevertheless, skin closure alone might not be sufficient to fulfill the criteria of successful defect reconstruction. In case of moderate or insufficient wound conditions, wound bed preparation is necessary. If wound bed preparation is successful and good wound conditions can be achieved, skin grafting is possible. If, however, this attempt is unsuccessful and moderate or binadequate wound conditionsQ are persisting, other methods of defect reconstruction such as local flap transfer, distant flap transfer, free (microvascular) flaps, and ultimately amputation must be considered.

In this research statistic analyses of Web traffic were carried out based on Empirical Distribution Function (EDF) test. Several probability distributions, such as Pareto (simple), extreme value, Weibull (three parameters), exponential, logistic, Pareto (generalized) have been chosen to fit the experimental traffic data (traces) which show an analytical indication of traffic behaviour. The issues of traffic characterisation and performance shown by these models have been discussed in terms of heavy tailedness and fitness of the curves. The aim of this research is to find a suitable analytical method which can characterise the Web traffic.

-Depuis quelques années, la théorie des valeurs extrêmes a reçu beaucoup d'attention aussi bien sur le plan théorique que sur le plan pratique. Les domaines d'applications sont en effet très variés : hydrologie, météorologie, biologie, ingénierie, gestion de l'environnement, finance, assurance, sciences sociales, etc. ; en effet la gestion des risques est devenue aujourd'hui fondamentale dans tous ces domaines. Cependant, ce type d'analyse basé sur la théorie des valeurs extrêmes est limité, voire très limité pour analyser les risques encourus sur le marché pétrolier alors que ces techniques peuvent sans doute aider à l'étude quantitative des risques. Le succès croissant de cette théorie nous a incité à mieux explorer son apport en matière de la gestion des fluctuations extrêmes sur le marché pétrolier. MOTS-CLÉS-Analyse de sensibilité, Gestion des risques, Loi de Pareto généralisée, Pétrole, Théorie des valeurs extrêmes, « Value at Risk » SUMMARY-Fundamentals of extreme value theory, its principal applications and its contribution to the risk management of the oil market For many years, Extreme value theory has received much attention on the theoretical level as well as on the practical one. The scope of its applications are indeed very varied and include hydrology, meteorology, biology, engineering, environmental management, finance, insurance, social life, etc. since risk management has become fundamental today in all these fields. However, this type of analysis based on the extreme value theory is little, even very limited to analyze the risks incurred on oil market whereas these techniques can undoubtedly help in a quantitative study of the risks. The increasing success of this theory in many fields encouraged us to better investigate its contribution to risk management of extreme fluctuations on crude oil market.

Background: Utilization is used as the principal marker of theatre performance in the NHS. This study investigated its validity as: a managerial tool, an inter-Trust indicator of efficient theatre use and as a marker of service performance for surgeons.

ABSTRACT: The present paper examines how statistics of extremes can be used to enhance the assessment and performance prediction of monitored highway bridges. This is achieved by proposing an approach to obtain a monitoring-based live-load for use in a reliability analysis. Time effects that correlate observed data to code required return periods are considered. Additionally, a method to identify, minimise and properly account for the epistemic uncertainty inherent to any monitoring record within a reliability analysis is presented. The approach can be utilised to plan data collection efforts or to maximise the utility of a limited amount of data. The extension of extreme value statistics to the monitoring of highway bridges is developed first using simulations and is then demonstrated on a case study using 90 days of in-service data collected from a bridge located in Pennsylvania, USA.

KEYWORDS: monitoring; statistics of extremes; reliability assessment; uncertainty; live loads; highway bridges

An uncertainty analysis of the unsteady flow component (UNET) of the one-dimensional model HEC-RAS within the generalised likelihood uncertainty estimation (GLUE) is presented. For this, the model performance of runs with different sets of Manning roughness coefficients, chosen from a range between 0.001 and 0.9, are compared to inundation data and an outflow hydrograph. The influence of variation in the weighting coefficient of the numerical scheme is also investigated. For the latter, the empirical results show no advantage of using values below 1 and suggest the use of a fully implicit scheme (weighting parameter equals 1). The results of varying the reach scale roughnesses shows that many parameter sets can perform equally well (problem of equifinality) even with extreme values. However, this depends on the model region and boundary conditions. The necessity to distinguish between effective parameters and real physical parameters is emphasised. The study demonstrates that this analysis can be used to produce dynamic probability maps of flooding during an event and can be linked to a stopping criterion for GLUE.

Surface hardened components are used in fatigue critical applications such as axles and gears. Inclusions are critical microstructural features where fatigue cracks have been observed to nucleate in these parts. In this investigation, the effect of inclusion populations on fatigue performance of induction hardened 1045 steel was examined. The steel was heat treated to have a tempered martensite starting microstructure and was induction hardened to two different case depths. Utilizing extreme value statistical analysis, the largest inclusion as well as the largest inclusion in each of five categories, MnS, MnCaS, MnAlS, Al 2 O 3 , and Al 2 O 3 -MgO, was estimated for a critically stressed area in a fully reversed cantilever bending fatigue sample. The inclusion size estimates were used to predict the endurance limit of the sample with a fracture mechanics-based model. This methodology has been traditionally used for homogeneous materials but has been modified here for bending fatigue and inhomogeneous case hardened material. The predicted endurance limits are closely correlated to experimentally measured endurance limits.

Productive wetland systems at land–water interfaces that provide unique ecosystem services are challenging to study because of water dynamics, complex surface cover and constrained field access. We applied object-based image analysis and supervised classification to four 32-m Beijing-1 microsatellite images to examine broad-scale surface cover composition and its change during November 2007–March 2008 low water season at Poyang Lake, the largest freshwater lake-wetland system in China (> 4000 km2). We proposed a novel method for semi-automated selection of training objects in this heterogeneous landscape using extreme values of spectral indices (SIs) estimated from satellite data. Dynamics of the major wetland cover types (Water, Mudflat, Vegetation and Sand) were investigated both as transitions among primary classes based on maximum membership value, and as changes in memberships to all classes even under no change in a primary class. Fuzzy classification accuracy was evaluated as match frequencies between classification outcome and a) the best reference candidate class (MAX function) and b) any acceptable reference class (RIGHT function). MAX-based accuracy was relatively high for Vegetation (≥ 90%), Water (≥ 82%), Mudflat (≥ 76%) and the smallest-area Sand (≥ 75%) in all scenes; these scores improved with the RIGHT function to 87–100%. Classification uncertainty assessed as the proportion of fuzzy object area within a class at a given fuzzy threshold value was the highest for all classes in November 2007, and consistently higher for Mudflat than for other classes in all scenes. Vegetation was the dominant class in all scenes, occupying 41.2–49.3% of the study area. Object memberships to Vegetation mostly declined from November 2007 to February 2008 and increased substantially only in February–March 2008, possibly reflecting growing season conditions and grazing. Spatial extent of Water both declined and increased during the study period, reflecting precipitation and hydrological events. The “fuzziest” Mudflat class was involved in major detected transitions among classes and declined in classification accuracy by March 2008, representing a key target for finer-scale research. Future work should introduce Vegetation sub-classes reflecting differences in phenology and alternative methods to discriminate Mudflat from other classes. Results can be used to guide field sampling and top-down landscape analyses in this wetland.► We present wetland object-based analysis and change detection at Poyang Lake, China. ► We propose novel methods to select training objects and analyze class uncertainty. ► Important fuzzy membership changes were detected even with no primary class change. ► Changes in Vegetation class membership reflected grazing and temperature variation. ► The fuzziest Mudflat class was sensitive to flooding and needs finer-scale research.

The boxplot method (Exploratory Data Analysis, Addison-Wesley, Reading, MA, 1977) is a graphically-based method of identifying outliers which is appealing not only in its simplicity but also because it does not use the extreme potential outliers in computing a measure of dispersion. The inner and outer fences are deÿned in terms of the hinges (or fourths), and therefore are not distorted by a few extreme values. Such distortion could lead to failing to detect some outliers, a problem known as "masking".

There is an increasing interest towards synthetic closures as an alternative to cork stoppers for sealing wine bottles. In this preliminary study, a set of testing conditions using the TA-HDI Texture Analyzer were implemented to measure selected mechanical parameters for the characterization of wine closures (natural and technical corks, co-extruded and injected synthetic closures in terms of compression force, extraction force and resilience. The results showed the presence of significant differences among the closures for the parameters tested. Injected closures were characterized by the highest weight (range = 6.8–7.2 g), whereas the corks showed wide variability (SD = 0.23–0.57 = 4.4–15.3%). The force required to pull-out the closure from the bottle ranged between 176 and 421 N and the extreme values were found on natural (196 ± 20 N) and technical cork (329 ± 39 N). The force of compression was highest for corks (1006–1046 N), whereas lowest values were found for the synthetic closures (566–639 N). The Principal Component Analysis grouped the synthetic closures according to the technology process, i.e. injected and co-extruded, whereas the corks broadened aside with a little dispersion of technical cork compared to the natural cork.

In mid 2004, after a lengthy period of industry consultation, the Basel Committee finally released its definitive rules on capital charges for Operational Risk under Basel II. In its proposals for allowing banks to calculate regulatory capital using their own internal models, the Basel Committee specified very stringent 'quantitative standards' for modelling operational risk. This has led to much discussion in the industry as to the types of statistical tools that could be used to calculate operational risk capital, under the so-called Loss Distribution Approach (LDA). Advanced techniques, such as Extreme Value Theory (EVT), have been proposed to satisfy the new regulatory requirements.

The statistics of extremes have played an important role in engineering practice for water resources design and management. How recent developments in the statistical theory of extreme values can be applied to improve the rigor of hydrologic applications and to make such analyses more physically meaningful is the central theme of this paper. Such methodological developments primarily relate to maximum likelihood estimation in the presence of covariates, in combination with either the block maxima or peaks over threshold approaches. Topics that are treated include trends in hydrologic extremes, with the anticipated intensification of the hydrologic cycle as part of global climate change. In an attempt to link downscaling (i.e., relating large-scale atmosphereocean circulation to smaller-scale hydrologic variables) with the statistics of extremes, statistical downscaling of hydrologic extremes is considered. Future challenges are reviewed, such as the development of more rigorous statistical methodology for regional analysis of extremes, as well as the extension of Bayesian methods to more fully quantify uncertainty in extremal estimation. Examples include precipitation and streamflow extremes, as well as economic damage associated with such extreme events, with consideration of trends and dependence on patterns in atmosphere-ocean circulation (e.g., El Niñ no phenomenon).

This research entails the implications of risk of unemployment and  underemployment of insurance companies in Kitui county .We are trying to come up with ways and mechanisms to  reduce these implications  and determine the correlation existing between the risk implications and growth of insurance companies in the region. The study of unemployment and underemployment are important not only because of their impact on economic assumptions but also their direct impact in the insurance industry. A deep understanding of the two concepts will help us in economic focus, insurance assumptions and risk management.
Labor markets is an absolutely necessary component of economic system since it affects other economic systems and therefore the economic environment, it also determines employment income which affects consumption, policy holder behavior and  Insurance  assumptions such as sales volume, lapse rate, and premium persistency.
Thus it is beneficial to analyze the impact of unemployment and underemployment in Kitui County.

A widely-noted change in the North Atlantic circulation in the 1970s affected 2 the spatial distribution and seasonal pattern of rainfall over Ireland. To examine if 3 this was accompanied by a change on short duration precipitation extremes, multi-4 decadal time series from the second half of the twentieth century of thirteen hourly 5 precipitation stations in Ireland have been analysed for the occurrence of extreme 6 values over several durations of up to 24 hours. Strong evidence was found for 7 a change since the late 1970s in short duration rainfall depths, particularly in the 8 west of the country. Precipitation depth-duration-frequency analyses over two 9 sub-periods showed that at several locations, storm event magnitudes which cor-10 responded to a 30 year return period before 1975 had a return period close to 11 10 years in the post-1975 period. The widespread increase in spring and autumn 12 rainfall and the local increases in the frequencies and magnitudes of severe rain-13 falls have implications for engineering hydrology, flood risk analysis and water 14 resources management. The necessity of using up-to-date data to derive design 15 storm magnitudes is stressed, due to the possible influence of underlying climatic 16 shifts. Furthermore, as non-stationarity has been demonstrated, the use of long 17 timeseries extending beyond thirty years into the past will result in underestima-18 tion of storm intensities in many areas.

CAÑELLAS, B.; ORFILA, A.; MÉNDEZ, F.J.; MENÉNDEZ, M. and TINTORÉ, J., 2007. Application of a POT model to estimate the extreme significant wave height levels around the Extreme value wave climate analysis at a particular site requires predicting long-term wave height levels from short duration records. In the present work we used the Peak Over Threshold (POT) model, assuming the frequency as a Poisson process and the intensity to be Pareto distributed, to characterize the spatial variability of the long-term extreme value wave climate along the Balearic Sea. Wave data used is part of the HIPOCAS database, a 44-years high resolution, spatial and temporal, wave hindcast, covering an area between 38ºN-42ºN and 1ºW-6ºE, of the western Mediterranean Sea. The use of data from a homogeneous grid, instead of a single location wave data record, allows describing the spatial variability of the long-term extreme wave height levels, over the whole Balearic Basin. Results show that extreme values for a 50-year return period level around 11 m are found in the north sector of the Balearic Islands while in the southern part much lower extreme values are found. This is due to the shadow effect of the islands over the severe north-eastern storms.

The carbon footprint (CF) of milk production was analysed at the farm gate for two contrasting production systems; an outdoor pasture grazing system in New Zealand (NZ) and a mainly indoor housing system with pronounced use of concentrate feed in Sweden (SE). The method used is based on the conceptual framework of lifecycle assessment (LCA), but only for greenhouse gas (GHG) emissions. National average data were used to model the dairy system in each country. Collection of inventory data and calculations of emissions were harmonised to the greatest extent possible for the two systems. The calculated CF for 1 kg of energy corrected milk (ECM), including related by-products (surplus calves and culled cows), was 1.00 kg carbon dioxide equivalents (CO 2 e) for NZ and 1.16 kg CO 2 e for SE. Methane from enteric fermentation and nitrous oxide emissions from application of nitrogen (as fertiliser and as excreta dropped directly on the field) were the main contributors to the CF in both countries. The most important parameters to consider when calculating the GHG emissions were dry matter intake (DMI), emission factor (EF) for methane from enteric fermentation, amount of nitrogen applied and EF for direct nitrous oxide emissions from soils. By changing one parameter at a time within 'reasonable' limits (i.e. no extreme values assumed), the impact on the total CF was assessed and showed changes of up to 15%. In addition, the uncertainty in CF estimates due to uncertainty in EF for methane from enteric fermentation and nitrous oxide emissions (from soil and due to ammonia volatilisation) were analysed through Monte Carlo simulation. This resulted in an uncertainty distribution corresponding to 0.60-1.52 kg CO 2 e kg À1 ECM for NZ and 0.83-1.56 kg CO 2 e kg À1 ECM for SE (in the prediction interval 2.5-97.5%). Hence, the variation within the systems based on the main EF is relatively large compared with the difference in CF between the countries.

.   In this paper, an additional entropy penalty term is used to steer the direction of the hidden node's activation in the process of learning. A state with minimum entropy means that most nodes are operating in the non-linear zones (i.e. saturation zones) near the extreme ends of the Sigmoid curve. As the training proceeds, redundant hidden nodes' activations are

Using methods from extreme value theory, we examine the major pandemics in history, trying to understand their tail properties. Applying the shadow distribution approach developed by the authors for violent conflicts [5], we provide rough estimates for quantities not immediately observable in the data. Epidemics and pandemics are extremely heavy-tailed, with a potential existential risk for humanity. This property should override conclusions derived from local epidemiological models in what relates to tail events.