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A warming climate is associated with increasing hydroclimatic extremes, which are often interconnected through complex processes, prompting their concurrence and/or succession, and causing compound extreme events. It is critical to analyze the risks of compound events, given their disproportionately high adverse impacts. To account for the variability in two or more hydroclimatic variables (e.g., temperature and precipitation) and their dependence, a rising number of publications focuses on multivariate analysis, among which the notion of copula‐based probability distribution has attracted tremendous interest. Copula is a mathematical function that expresses the joint cumulative probability distribution of multiple variables. Our focus is to re‐emphasize the fundamental requirements and limitations of applying copulas. Confusion about these requirements may lead to misconceptions and pitfalls, which can potentially compromise the robustness of risk analyses for environmental processes and natural hazards. We conducted a systematic literature review of copulas, as a prominent tool in the arsenal of multivariate methods used for compound event analysis, and underpinned them with a hydroclimatic case study in Sweden to illustrate a practical approach to copula‐based modeling. Here, we (1) provide end‐users with a didactic overview of necessary requirements, statistical assumptions and consequential limitations of copulas, (2) synthesize common perceptions and practices, and (3) offer a user‐friendly decision support framework to employ copulas, thereby support researchers and practitioners in addressing hydroclimatic hazards, hence demystify what can be an area of confusion. This article is categorized under:Science of Water > Hydrological ProcessesScience of Water > Methods [ABSTRACT FROM AUTHOR]

Mamdani fuzzy inference system has been widely used for potential risk modelling and management. The decision-making is usually provided by multiple experts in the field. The conflicting information in sources from different experts become an open issue and has attracted some researchers to investigate further. Various risk factors in a project caused difficulties for decision makers to make reliable decisions on the whole project since it involves ambiguities, vagueness, and fuzziness. The introduction of the fuzzy inference system to the evaluation of construction risk is capable in explaining its reasoning process and, hence, overcoming such problems. Risk factors under the project management risk were identified through literature sources and from the opinion of experts. It is found that the likelihood and severity of risk is somehow interlinked with the concept of fuzzy theory. For model input and output linguistics variables, the triangular membership function was selected. The methodology employs a fuzzy aggregation system in which an appropriate control action can be determined by the acquisition of expert judgment. A total of 23 rules with logical OR operator, truncation implication, and Mean of Maxima (MoM) method for defuzzification were used to create an effective fuzzy model intended for making decisions. The framework determines the relationship between input and output parameters in if-then rules or mathematical functions using an effective fuzzy arithmetic operator. The study addresses the principle issues of multiexpert opinions based on Mamdani-type decision system and the illustrative example taken from one of medium-sized project held in Malaysia's construction industry. By comparing with other experimental results, we verify the rationality and reliability of the proposed method. [ABSTRACT FROM AUTHOR]

Mamdani fuzzy inference system has been widely used for potential risk modelling and management. The decision-making is usually provided by multiple experts in the field. The conflicting information in sources from different experts become an open issue and has attracted some researchers to investigate further. Various risk factors in a project caused difficulties for decision makers to make reliable decisions on the whole project since it involves ambiguities, vagueness, and fuzziness. The introduction of the fuzzy inference system to the evaluation of construction risk is capable in explaining its reasoning process and, hence, overcoming such problems. Risk factors under the project management risk were identified through literature sources and from the opinion of experts. It is found that the likelihood and severity of risk is somehow interlinked with the concept of fuzzy theory. For model input and output linguistics variables, the triangular membership function was selected. The methodology employs a fuzzy aggregation system in which an appropriate control action can be determined by the acquisition of expert judgment. A total of 23 rules with logical OR operator, truncation implication, and Mean of Maxima (MoM) method for defuzzification were used to create an effective fuzzy model intended for making decisions. The framework determines the relationship between input and output parameters in if-then rules or mathematical functions using an effective fuzzy arithmetic operator. The study addresses the principle issues of multiexpert opinions based on Mamdani-type decision system and the illustrative example taken from one of medium-sized project held in Malaysia's construction industry. By comparing with other experimental results, we verify the rationality and reliability of the proposed method. [ABSTRACT FROM AUTHOR]

The construction of large renewable energy projects is characterized by the great uncertainties associated with their administrative complexity and their constructive characteristics. For proper management, it is necessary to undertake a thorough project risk assessment prior to construction. The work presented in this paper is based on a hierarchical risk structure identified by a group of experts, from which a Probabilistic Fuzzy Sets with Analysis Hierarchy Process (PFSAHP) was applied. This probabilistic analysis approach used expert opinion based on the Monte Carlo Method that allows for extracting more information from the original data. In addition, the coherence of the experts’ opinions is assessed using a novel parameter known as Confidence Level, which allows for adjusting the opinions of experts and weighting their judgments regarding impact and probability according to their coherence. This model has the advantage of offering a risk analysis in the early stages of the management of renewable energy projects in which there is no detailed information. This model is also more accurate than the classic fuzzy methodology when working with complete distribution functions, whilst it avoids the loss of information that results from the traditional mathematical operations with Fuzzy numbers. To test the model, it was applied to a 250 MW photovoltaic solar plant construction project located in southeast of Spain (Region of Murcia). As a result of the application of the proposed method, risk rankings are obtained with respect to the cost, the time, the scope and from a general point of view of the project. [ABSTRACT FROM AUTHOR]

Aggregation functions and their transformations have found numerous applications in various kinds of systems as well as in economics and social science. Every aggregation function is known to be bounded above and below by its super-additive and sub-additive transformations. We are interested in the “inverse” problem of whether or not every pair consisting of a super-additive function dominating a sub-additive function comes from some aggregation function in the above sense. Our main results provide a negative answer under mild extra conditions on the super- and sub-additive pair. We also show that our results are, in a sense, best possible. [ABSTRACT FROM AUTHOR]

It is well known that adaptive sequential nonparametric estimation of differentiable functions with assigned mean integrated squared error and minimax expected stopping time is impossible. In other words, no sequential estimator can compete with an oracle estimator that knows how many derivatives an estimated curve has. Differentiable functions are typical in probability density and regression models but not in spectral density models, where considered functions are typically smoother. This paper shows that for a large class of spectral densities, which includes spectral densities of classical autoregressive moving average processes, an adaptive minimax sequential estimation with assigned mean integrated squared error is possible. Furthermore, a two-stage sequential procedure is proposed, which is minimax and adaptive to smoothness of an underlying spectral density. [ABSTRACT FROM AUTHOR]

With competing risks data, one often needs to assess the treatment and covariate effects on the cumulative incidence function. Fine and Gray proposed a proportional hazards regression model for the subdistribution of a competing risk with the assumption that the censoring distribution and the covariates are independent. Covariate-dependent censoring sometimes occurs in medical studies. In this paper, we study the proportional hazards regression model for the subdistribution of a competing risk with proper adjustments for covariate-dependent censoring. We consider a covariate-adjusted weight function by fitting the Cox model for the censoring distribution and using the predictive probability for each individual. Our simulation study shows that the covariate-adjusted weight estimator is basically unbiased when the censoring time depends on the covariates, and the covariate-adjusted weight approach works well for the variance estimator as well. We illustrate our methods with bone marrow transplant data from the Center for International Blood and Marrow Transplant Research. Here, cancer relapse and death in complete remission are two competing risks. [ABSTRACT FROM AUTHOR]

A new classifier for image data classification named as linear twin bounded support tensor machine (linear TBSTM) is proposed by adding regularization terms in objective functions, which results in the realization of structural risk minimization avoids of the singularity of matrices. We know that up to now nonlinear classifiers based on STM for image data classification are not seen more. In order to remedy this limitation, a new matrix kernel function is introduced and based on which the nonlinear version of TBSTM is studied with a detailed theoretical derivation, and then a nonlinear classifier called as nonlinear TBSTM is suggested. In order to examine the effectiveness of the proposed classifiers, a series of comparative experiments with three linear classifiers STM, TSTM and PSTM are performed on 15 binary image classification problems taken from ORL, YALE and AR datasets. Experiment results show that the proposed classifiers are effective and efficient. [ABSTRACT FROM AUTHOR]

Adverse Outcome Pathways (AOPs) are increasingly used to support the integration of in vitro data in hazard assessment for chemicals. Quantitative AOPs (qAOPs) use mathematical models to describe the relationship between key events (KEs). In this paper, data obtained in three cell lines, LHUMES, HepG2 and RPTEC/TERT1, using similar experimental protocols, was used to calibrate a qAOP of mitochondrial toxicity for two chemicals, rotenone and deguelin. The objectives were to determine whether the same qAOP could be used for the three cell types, and to test chemical-independence by cross-validation with a dataset obtained on eight other chemicals in LHUMES cells. Repeating the calibration approach for both chemicals in three cell lines highlighted various practical difficulties. Even when the same readouts of KEs are measured, the mathematical functions used to describe the key event relationships may not be the same. Cross-validation in LHUMES cells was attempted by estimating chemical-specific potency at the molecular initiating events and using the rest of the calibrated qAOP to predict downstream KEs: toxicity of azoxystrobin, carboxine, mepronil and thifluzamide was underestimated. Selection of most relevant readouts and accurate characterization of the molecular initiating event for cross-validation are critical when designing in vitro experiments targeted at calibrating qAOPs. [Display omitted] • A qAOP for mitochondrial toxicity was calibrated using in vitro data. • Data was collected in similar experimental setups in three cell lines. • The qAOP was calibrated for two chemicals and was mostly chemical-independent. • Validation with eight other chemicals cells was unsatisfactory in four chemicals. • Accurate characterization of the molecular initiating event is critical. [ABSTRACT FROM AUTHOR]

We discuss the optimal dividend and capital injection strategies in the Cramér-Lundberg risk model. The value function V(x) is defined by maximizing the discounted value of the dividend payment minus the penalized discounted capital injection until the time of ruin. It is shown that V(x) can be characterized by the Hamilton-Jacobi-Bellman equation. We find the optimal dividend barrier b, the optimal upper capital injection barrier 0, and the optimal lower capital injection barrier -z*. In the case of exponential claim size especially, we give an explicit procedure to obtain b, -z*, and the value function V(x). [ABSTRACT FROM AUTHOR]

The capability of a machine control system to perform a safety function is expressed using performance levels (PL). This paper presents the results of a study where PL estimation was carried out for a safety function implemented using three different distributed control system structures. Challenges relating to the process of estimating PLs for safety related distributed machine control functions are highlighted. One of these examines the use of different cabling schemes in the implementation of a safety function and its effect on the PL evaluation. The safety function used as a generic example in PL calculations relates to a mobile work machine. It is a safety stop function where different technologies (electrical, hydraulic and pneumatic) can be utilized. It was detected that by replacing analogue cables with digital communication the system structure becomes simpler with less number of failing components, which can better the PL of the safety function. [ABSTRACT FROM AUTHOR]

In a dependent competing risks model is impossible to determine the marginal distributions from the competing risks data alone. This is known as the identifiability problem. Zheng and Klein (1995) propose the copula graphic estimator as a solution to the identifiability problem for two competing risks. For that, they assume a dependence structure using a copula for the joint distribution of failure times and its dependence parameter known. Lo and Wilke (2010) propose the risk pooling method as an extension of the copula graphic estimator when the copula is Archimedean. This research for the trivariate case, is compared the true joint survival function, with joint survival function estimated assuming independence among failure times and the survival function estimated by the risk pooling method. These comparisons are performed via simulation considering failure times associated with multivariate Weibull and lognormal distributions and different levels of dependence between failure times. We conclude that the estimator assuming independence is less efficient than the estimator of the survival function using the risk pooling method. The methodology is illustrated with reliability data of FL245 switches in Interconexión Eléctrica S.A. E.S.P. (ISA), which show the usefulness of this topic in industrial reliability. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a new three-parameters lifetime distribution with unimodal, increasing and decreasing hazard rate. The new distribution, the complementary Weibull geometric (CWG), is complementary to the Weibull-geometric (WG) model proposed by Barreto-Souzaet al.(The Weibull-Geometric distribution, J. Statist. Comput. Simul. 1 (2010), pp. 1–13). The CWG distribution arises on a latent complementary risks scenarios, where the lifetime associated with a particular risk is not observable, rather we observe only the maximum lifetime value among all risks. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its reliability and hazard rate functions, moments, density of order statistics and their moments. We provide expressions for the Rényi and Shannon entropies. The parameter estimation is based on the usual maximum likelihood approach. We obtain the observed information matrix and discuss inferences issues. We report a hazard function comparison study between the WG distribution and our complementary one. The flexibility and potentiality of the new distribution is illustrated by means of three real dataset, where we also made a comparison between Weibull, WG and CWG modelling approach. [ABSTRACT FROM AUTHOR]

Consider a portfolio of n identically distributed risks X1, …, Xn with dependence structure modelled by an Archimedean survival copula. It is known that the probability of a large aggregate loss of $\sum\nolimits_{i=1}^{n} X_{i}$ is in proportion to the probability of a large individual loss of X1. The proportionality factor depends on the dependence strength and the tail behavior of the individual risk. In this paper, we establish analogous results for an aggregate loss of the form g(X1, …, Xn) under the more general model in which the Xi's have different but tail-equivalent distributions and the copula remains unchanged, where g is a homogeneous function of order 1. Properties of these factors are studied, and asymptotic Value-at-Risk behaviors of functions of dependent risks are also given. The main results generalize those in Wüthrich [16], Alink, Löwe, and Wüthrich [2], Barbe, Fougères, and Genest [4], and Embrechts, Nešlehová, and Wüthrich [9]. [ABSTRACT FROM AUTHOR]

Abstract: For the estimation of the radiation risk for astronauts, not only the organ absorbed doses but also their mean quality factors must be evaluated. Three functions have been proposed by different organizations for expressing the radiation quality, including the Q(L), Q(y), and Q NASA(Z, E) relationships as defined in International Committee of Radiological Protection (ICRP) Publication 60, International Commission on Radiation Units and Measurements (ICRU) Report 40, and National Aeronautics and Space Administration (NASA) TP-2011-216155, respectively. The Q(L) relationship is the most simple and widely used for space dosimetry, but the use of the latter two functions enables consideration of the difference in the track structure of various charged particles during the risk estimation. Therefore, we calculated the mean quality factors in organs and tissues in ICRP/ICRU reference voxel phantoms for the isotropic exposure to various mono-energetic particles using the three Q-functions. The Particle and Heavy Ion Transport code System PHITS was employed to simulate the particle motions inside the phantoms. The effective dose equivalents and the phantom-averaged effective quality factors for the astronauts were then estimated from the calculated mean quality factors multiplied by the fluence-to-dose conversion coefficients and cosmic-ray fluxes inside a spacecraft. It was found from the calculations that Q NASA generally gives the largest values for the phantom-averaged effective quality factors among the three Q-functions for neutron, proton, and lighter-ion irradiation, whereas Q(L) provides the largest values for heavier-ion irradiation. Overall, the introduction of Q NASA instead of Q(L) or Q(y) in astronaut dosimetry results in the increase the effective dose equivalents because the majority of the doses are composed of the contributions from protons and neutrons, although this tendency may change by the calculation conditions. [Copyright &y& Elsevier]

We consider a Sparre Andersen risk model perturbed by diffusion where the interclaim times are generalized Erlang(n) distribution. Generalized discounted penalty functions incorporating the maximum surplus before ruin are studied. We derive the integrodifferential equations and give the solutions for the generalized discounted penalty functions. [ABSTRACT FROM AUTHOR]

In this paper, we study a risk model with two independent classes of risks, in which both claim number processes are renewal processes with phasetype inter-arrival times. Using a generalized matrix Dickson-Hipp operator, a matrix Volterra integral equation for the Gerber-Shiu function is derived. And the analytical solution to the Gerber-Shiu function is also provided. [ABSTRACT FROM AUTHOR]

Abstract: Multi-objective optimization for designing of a small-scale distributed CCHP system has been performed. Small-scale combined cooling, heating, and power generation technologies represent a key resource to increase generation efficiency and reduce greenhouse gas emissions with respect to conventional separate production means. In the multi-objective optimization of the small-scale distributed CCHP system, the three objective functions including the exergetic efficiency, total levelized cost rate of the system product and the cost rate of environmental impact have been considered. The environmental impact objective function has been defined and expressed in cost terms however this objective has not been integrated with the thermoeconomic objective. The thermodynamic modeling has been implemented comprehensively while the economic analysis conducted in accordance with the total revenue requirement (TRR) method. One of the most suitable optimization techniques namely as genetic algorithm has been applied to find the set of Pareto optimal solutions with respect to the aforementioned objective functions. In the present work, reliability and availability are introduced in the thermoenvironomic model of the system, so that redundancy is embedded in the optimal solution. Risk analysis is used for decision-making of the final optimal solution from the obtained Pareto optimal frontier. [Copyright &y& Elsevier]

In risk analysis, the mean excess plot is a commonly used exploratory plotting technique for confirming iid data is consistent with a generalized Pareto assumption for the underlying distribution since in the presence of such a distribution, thresholded data have a mean excess plot that is roughly linear. Does any other class of distributions share this linearity of the plot? Under some extra assumptions, we are able to conclude that only the generalized Pareto family has this property. [ABSTRACT FROM AUTHOR]

The increased deformation and shear fragilities of corroding RC bridge columns subject to seismic excitations are modeled as functions of time using fragility increment functions. These functions can be applied to various environmental and material conditions by means of controlling parameters that correspond to the specific condition. For each mode of failure, the fragility of a deteriorated column at any given time is obtained by simply multiplying the initial fragility of the pristine/nondeteriorated column by the corresponding function developed in this paper. The developed increment functions account for the effects of the time-dependent uncertainties that are present in the corrosion model as well as in the structural capacity models. The proposed formulation is a useful tool for engineering practice because the fragility of deteriorated columns is obtained without any extra reliability analysis once the fragility of the pristine column is known. The fragility increment functions are expressed as functions of time t and a given deformation or shear demand. Unknown parameters involved in the models are estimated using a Bayesian updating framework. A model selection is conducted during the assessment of the unknown parameters using the Akaike information criterion and the Bayesian information criterion. For the estimation of the parameters, a set of data are obtained by first-order reliability method analysis using existing probabilistic capacity models for corroding RC bridge columns. Example fragilities of a deteriorated bridge column typical of current California’s practice are presented to demonstrate the developed methodology. The increment functions suggested in this paper can be used to assess the time-variant fragility for application to life cycle cost analysis and risk analysis. [ABSTRACT FROM AUTHOR]

This paper presents fuzzy-probabilistic modeling techniques for system component outage parameters and load curves. The fuzzy membership functions of systeiu component outage parameters are developed using statistical records, whereas the system load is modeled using a combined fuzzy and probabilistic representation. Based on the fuzzy-probabilistic models, a hybrid method of fuzzy set and Monte Carlo simulation for power system risk assessment is proposed to capture both randomness and fuzziness of loads and component outage parameters. An actual example using a regional system at the British Columbia Transmission Corpoation is given to demonstrate the application of the presented fuzzy-probabilistic models for system parameters and new system risk evaluation method. [ABSTRACT FROM AUTHOR]

Tight bounds are derived on the risk of models in the ensemble generated by incremental training of an arbitrary learning algorithm. The result is based on proof techniques that are remarkably different from the standard risk analysis based on uniform convergence arguments, and improves on previous bounds published by the same authors. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers the delayed renewal risk model with random premium income. The Gerber–Shiu discounted penalty function in the delayed renewal model is expressed in terms of the corresponding Gerber–Shiu function in the ordinary renewal model. The obtained results can be viewed as the discrete analogy of the classical Sparre–Anderson risk model. [Copyright &y& Elsevier]

We consider the case where a terminal event censors a non-terminal event, but not vice versa. When the events are dependent, estimation of the distribution of the non-terminal event is a competing risks problem, while estimation of the distribution of the terminal event is not. The dependence structure of the event times is formulated with the gamma frailty copula on the upper wedge, with the marginal distributions unspecified. With a consistent estimator of the association parameter, pseudo self-consistency equations are derived and adapted to the semiparametric model. Existence, uniform consistency and weak convergence of the new estimator for the marginal distribution of the non-terminal event is established using theories of empirical processes,U-statistics andZ-estimation. The potential practical utility of the methodology is illustrated with simulated and real data sets. [ABSTRACT FROM AUTHOR]

On of the most important types of system structures is the parallel structure. In the present article, we propose a definition for the mean residual life function of a parallel system and obtain some of its properties. The proposed definition measures the mean residual life function of a parallel system consisting of a identical and independent components under the condition that n - i, i = 0,2, …, n - 1, components of the system are working and other components of the system have already failed. It is shown that, for the case where the components of the system have increasing hazard rate, the mean residual life function of the system is a nonincreasing function of time. Finally, we will obtain an upper bound for the proposed mean residual life function. [ABSTRACT FROM AUTHOR]

In this paper we explore the approximation of the normal density function with the triangular density function, a density function that has extensive use in risk analysis. Such an approximation generates a simple piecewise-linear density function and a piecewise-quadratic distribution function that can be easily manipulated mathematically and that produces surprisingly accurate performance under many instances. This mathematical tractability proves useful when it enables closed-form solutions not otherwise possible, as with problems involving the embedded use of the normal density. For benchmarking purposes we compare the basic triangular approximation with two flared triangular distributions and with two simple uniform approximations; however, throughout the paper our focus is on using the triangular density to approximate the normal for reasons of parsimony. We also investigate the logical extensions of using a non-symmetric triangular density to approximate a lognormal density. Several issues associated with using a triangular density as a substitute for the normal and lognormal densities are discussed, and we explore the resulting numerical approximation errors for the normal case. Finally, we present several examples that highlight simple decision rules-of-thumb that the use of the approximation generates. Such rules-of-thumb, which are useful in risk and reliability analysis and general business analysis, can be difficult or impossible to extract without the use of approximations. These examples include uses of the approximation in generating random deviates, uses in mixture models for risk analysis, and an illustrative decision analysis problem. It is our belief that this exploratory look at the triangular approximation to the normal will provoke other practitioners to explore its possible use in various domains and applications. [Copyright &y& Elsevier]

Integral models for heavy gas dispersion approximate a dispersing cloud in terms of a small number of variables; each of these is ultimately a function of an independent variable which is usually time (instantaneous releases) or downwind distance (continuous releases).This type of model is used almost exclusively in risk assessment [HSE’s risk assessment tool, RISKAT, in: Major Hazards: Onshore and Offshore, October 1992, pp. 607–638; Ann. Rev. Fluid Mech. 21 (1989) 317], but many distinct integral models exist. The code comparison exercise of Mercer et al. [CEA/AEA exchange agreement on external event. Comparison of heavy gas dispersion models for instantaneous releases: final report, Technical Report IR/L/HA/91/6, Health and Safety Laboratory, Sheffield, June 1991; J. Hazard. Mater. 36 (1994) 193] presented the results from a number of integral models in a common format; Mercer found that the range of predictions for some scenarios exceeded three orders of magnitude.Here, the TWODEE shallow layer model [J. Hazard. Mater. 66 (3) (1999) 211; J. Hazard. Mater. 66 (3) (1999) 227; J. Hazard. Mater. 66 (3) (1999) 239] is added to Mercer’s code comparison exercise. The physical assumptions used in shallow layer models differ profoundly from those used in integral models and the implications of these differences for risk assessment are discussed.TWODEE was used to simulate four representative cases considered by Mercer. In terms of cloud averaged concentration (CAC) vs. centroid position, the present model gave predictions that were consistent with the integral models used by Mercer.As the model neglects horizontal diffusion for passive clouds, overprediction at large downwind distances was expected, but not generally observed. [Copyright &y& Elsevier]

Nous considérons l'estimation de la moyenne θ d'une distribution sphérique avec une information a priori concernant la norme ||θ||. Le meilleur estimateur équivariant est obtenu pour le problème local ||θ|| = λ [ABSTRACT FROM AUTHOR]

We study the applicability of the half-normal distribution to the probability–severity risk analysis traditionally performed through risk matrices and continuous probability–consequence diagrams (CPCDs). To this end, we develop a model that adapts the financial risk measures Value-at-Risk (VaR) and Conditional Value at Risk (CVaR) to risky scenarios that face only negative impacts. This model leads to three risk indicators: The Hazards Index-at-Risk (HIaR), the Expected Hazards Damage (EHD), and the Conditional HIaR (CHIaR). HIaR measures the expected highest hazards impact under a certain probability, while EHD consists of the expected impact that stems from truncating the half-normal distribution at the HIaR point. CHIaR, in turn, measures the expected damage in the case it exceeds the HIaR. Therefore, the Truncated Risk Model that we develop generates a measure for hazards expectations (EHD) and another measure for hazards surprises (CHIaR). Our analysis includes deduction of the mathematical functions that relate HIaR, EHD, and CHIaR to one another as well as the expected loss estimated by risk matrices. By extending the model to the generalised half-normal distribution, we incorporate a shape parameter into the model that can be interpreted as a hazard aversion coefficient. [ABSTRACT FROM AUTHOR]