Open Access

Conditional excess distribution modelling is a widely used technique, in financial and insurance mathematics or survival analysis, for instance. Classical theory considers the thresholds as fixed values. In contrast, the use of empirical quantiles as thresholds offers advantages with respect to the design of the statistical experiment. Either way, the modeller is in a non-standard situation and runs in the risk of improper usage of statistical procedures. From both points of view, statistical planning and inference, a detailed discussion is requested. For this purpose, we treat both methods and demonstrate the necessity taking into account the characteristics of the approaches in practice. In detail, we derive general statements for empirical processes related to the conditional excess distribution in both situations. As examples, estimating the mean excess and the conditional Value-at-Risk are given. We apply our findings for the testing problems of goodness-of-fit and homogeneity for the conditional excess distribution and obtain new results of outstanding interest.

The paper presents a study dealing with the assessment of the dynamic overpressure induced by earthquakes in flat bottom steel silos. Silos are integral components of industrial plants, as part of a complex network of mechanical and structural components. Ensuring the safety of silos is critical in industrial processes, especially when the action of hazardous events (e.g., earthquakes) can mine their structural stability and, subsequently, the stored material. In this view, a robust and reliable design approach is crucial for civil engineering professionals, which need to properly understand and predict the dynamic conditions to which silos are subjected, especially under seismic excitations. The current European standard, EN 1998-4-2006, employs a static approach using equivalent loads to simulate the additional hydrodynamic seismic pressure. However, a more realistic estimation of additional seismic overpressure could yield a more rational steel wall analysis and design for new structures and assessment for existing structures. To this end, this paper presents detailed numerical analyses to estimate the dynamic overpressure experienced by silos wall under seismic excitation. In detail, finite element models were created for two geometries of silos, i.e., slender and squat, and nonlinear time history analyses were carried out. The detailed models accounted for geometrical and mechanical nonlinearity of steel silos and of stored granular-like solid material. This latter was simulated by employing hypoplasticity as constitutive model. The output of the analyses allowed to quantify the additional dynamic pressure, which was compared to the one provided by the European standards (i.e., equivalent static approach). The comparison highlighted significant differences, underscoring the need to revise the current code-based approach.

There is a lack of fast and inexpensive analytical methods for quantification of key ingredients in dietary supplements. Here we explore the potential of near infrared (NIR) spectrometry, attenuated total reflection infrared (ATR-IR) spectrometry and potentiometric multisensor system (MSS) in quantitative determination of glucosamine and hyaluronic acid in commercial samples of dietary supplements. All three methods have demonstrated their applicability for this task when combined with chemometric data processing. Principal Component Analysis (PCA) revealed similarities across the three techniques, indicating the presence of distinct sample compositions. Partial least squares (PLS) models were constructed for glucosamine and hyaluronic acid quantification. The root mean square error of cross validation (RMSECV) for glucosamine quantification varied between 7.7 wt% and 8.9 wt%. NIR spectrometry has demonstrated the best accuracy for hyaluronic acid (RMSECV = 9.9 wt%), while ATR-IR and MSS yielded somewhat worse performance with RMSECV values of 12.1 and 11.3 wt%, respectively. The findings of this study indicated that NIR, ATR-IR and MSS exhibit reduced accuracy in comparison to complex and high-precision analytical techniques. However, they can be employed for the rapid, semi-quantitative evaluation of glucosamine and hyaluronic acid in dietary supplements, with the possibility of integration into routine quality control procedures.