Relative distribution analysis in Stata

In this article, I discuss the method of relative distribution analysis and present Stata software implementing various elements of the methodology. The relative distribution is the distribution of the relative ranks that the outcomes from one distribution take on in another distribution. The methodology can be used, for example, to compare the distribution of wages between men and women. The presented software, reldist, estimates the relative cumulative distribution and the relative density, as well as the relative polarization, divergence, and other summary measures of the relative ranks. It also provides functionality such as location and shape decompositions or covariate balancing. Statistical inference is implemented in terms of influence functions and supports estimation for complex samples.

Empirical influence functions and their non-standard applications

The main objective of the empirical influence function (EIF) is to describe how estimates behave when an observation set is affected by gross errors. Unlike the influence function, which represents the estimation method’s general properties, EIF can provide valuable information about applying different methods to a particular network. The chosen example allows us to compare different robust methods. The paper focuses on non-standard applications of EIF, for example, in assuming steering parameter of robust methods (usually related to the assumed interval for acceptable observation errors). The paper shows that commonly used values do not always work well, and EIFs might help choose appropriate values, guaranteeing the estimation process’s robustness. The most important new application of EIFs concerns the detection and assessment of a single gross error. The blinded experiments proved that such an approach is correct and can be an alternative to classic statistical tests for outlier detection.

Development of a Backward–Forward Stochastic Particle Tracking Model for Identification of Probable Sedimentation Sources in Open Channel Flow

As reservoirs subject to sedimentation, the dam gradually loses its ability to store water. The identification of the sources of deposited sediments is an effective and efficient means of tackling sedimentation problems. A state-of-the-art Lagrangian stochastic particle tracking model with backward–forward tracking methods is applied to identify the probable source regions of deposited sediments. An influence function is introduced into the models to represent the influence of a particular upstream area on the sediment deposition area. One can then verify if a specific area might be a probable source by cross-checking the values of influence functions calculated backward and forward, respectively. In these models, the probable sources of the deposited sediments are considered to be in a grid instead of at a point for derivation of the values of influence functions. The sediment concentrations in upstream regions must be known a priori to determine the influence functions. In addition, the accuracy of the different types of diffusivity at the water surface is discussed in the study. According to the results of the case study of source identification, the regions with higher sediment concentrations computed by only backward simulations do not necessarily imply a higher likelihood of sources. It is also shown that from the ensemble results when the ensemble mean of the concentration is higher, the ensemble standard deviation of the concentration is also increased.

Sensitivitätsanalyse mit verallgemeinerten Einflussfunktionen zur Tragwerksbewertung bei Modellparametervariationen/Sensitivity analysis with generalized influence functions for the treatment of model parameter variations in structural analysis

Der Beitrag handelt von der computergestützten Sensitivitätsanalyse, mit welcher eine systematische Bewertung der Empfindlichkeit von Antwortgrößen eines statischen Systems bei variierenden Modellparametern möglich ist. Konkret wird gezeigt, wie zur Berechnung von Sensitivitäten die Technik der Einflusslinien verallgemeinert werden kann. Die vorgeschlagene Generalisierung ermöglicht eine Erweiterung des klassischen Ansatzes für verschiedenste Systemantwortgrößen, Parameter und Strukturtypen und vereint somit numerische Methoden der Sensitivitätsanalyse mit klassischem Ingenieurverständnis bezüglich Einflusslinien. Der Aufsatz gewährt Einblicke in die theoretischen Hintergründe des Ansatzes und zeigt auf, wie die Ergebnisse graphisch aufbereitet werden können, um schnell und zielgerichtet wichtige Parameter hinsichtlich der betrachteten Systemantwortgröße zu identifizieren. Somit eignet sich die Methode als Hilfsmittel im Rahmen von Bemessung und Sicherheitsbeurteilung. Hierfür wird eine Analyse- und Entscheidungskette vorgeschlagen, welche dabei helfen soll, relevante Systemempfindlichkeiten zu identifizieren und beurteilen.