Sheffer sequences, probability distributions and approximation operators

We present a new method to compute formulas for the action on monomials of a generalization of binomial approximation operators of Popoviciu type, or equivalently moments of associated discrete probability distributions with finite support. These quantities are necessary to check the assumptions of the Korovkin Theorem for approximation operators, or equivalently the Feller Theorem for convergence of the probability distributions. Our method unifies and simplifies computations of well-known special cases. It only requires a few basic facts from Umbral Calculus. We illustrate our method to well-known approximation operators and probability distributions, as well as to some recent q-generalizations of the Bernstein approximation operator introduced by Lewanowicz and Wo´zny, Lupa¸s, and Phillips

A selected survey of umbral calculus

We survey the mathematical literature on umbral calculus (otherwise known as the calculus of finite differences) from its roots in the 19th century (and earlier) as a set of "magic rules" for lowering and raising indices, through its rebirth in the 1970’s as Rota’s school set it on a firm logical foundation using operator methods, to the current state of the art with numerous generalizations and applications. The survey itself is complemented by a fairly complete bibliography (over 500 references) which we expect to update regularly

Data-driven online monitoring of wind turbines

Condition based maintenance is a modern approach to maintenance which has been successfully used in several industrial sectors. In this paper we present a concrete statistical approach to condition based maintenance for wind turbine by applying ideas from statistical process control. A specific problem in wind turbine maintenance is that failures of a certain part may have causes that originate in other parts a long time ago. This calls for methods that can produce timely warnings by combining sensor data from different sources. Our method improves on existing methods used in wind turbine maintenance by using adaptive alarm thresholds for the monitored parameters that correct for values of other relevant parameters. We illustrate our method with a case study that shows that our method is able to predict upcoming failures much earlier than currently used methods

Small nonparametric tolerance regions

We present a new natural way to construct nonparametric multivariate tolerance regions. Unlike the classical nonparametric tolerance intervals, where the endpoints of the tolerance intervals are determined by beforehand chosen order statistics, we take the shortest interval, that contains a certain number of observations. We extend this idea to higher dimensions by replacing the class of intervals with other classes of sets, like ellipsoids, hyperrectangles or convex sets. The asymptotic behaviour of our tolerance regions is derived using empirical process theory, in particular the concept of generalized quantiles. Finite sample properties of our tolerance regions are investigated through a simulation study

Robust and Efficient Uncertainty Quantification and Validation of RFIC Isolation

Modern communication and identification products impose demanding constraints on reliability of components. Due to this statistical constraints more and more enter optimization formulations of electronic products. Yield constraints often require efficient sampling techniques to obtain uncertainty quantification also at the tails of the distributions. These sampling techniques should outperform standard Monte Carlo techniques, since these latter ones are normally not efficient enough to deal with tail probabilities. One such a technique, Importance Sampling, has successfully been applied to optimize Static Random Access Memories (SRAMs) while guaranteeing very small failure probabilities, even going beyond 6-sigma variations of parameters involved. Apart from this, emerging uncertainty quantifications techniques offer expansions of the solution that serve as a response surface facility when doing statistics and optimization. To efficiently derive the coefficients in the expansions one either has to solve a large number of problems or a huge combined problem. Here parameterized Model Order Reduction (MOR) techniques can be used to reduce the work load. To also reduce the amount of parameters we identify those that only affect the variance in a minor way. These parameters can simply be set to a fixed value. The remaining parameters can be viewed as dominant. Preservation of the variation also allows to make statements about the approximation accuracy obtained by the parameter-reduced problem. This is illustrated on an RLC circuit. Additionally, the MOR technique used should not affect the variance significantly. Finally we consider a methodology for reliable RFIC isolation using floor-plan modeling and isolation grounding. Simulations show good comparison with measurements

Symbolic computation and exact distributions of nonparametric test statistics

We show how to use computer algebra for computing exact distributions on nonparametric statistics. We give several examples of nonparametric statistics with explicit probability generating functions that can be handled this way. In particular, we give a new table of critical values of the Jonckheere-Terpstra test that extends tables known in the literature

Smallest nonparametric tolerance regions

We present a new, natural way to construct nonparametric multivariate tolerance regions. Unlike the classical nonparametric tolerance intervals, where the endpoints are determined by beforehand chosen order statistics, we take the shortest interval, that contains a certain number of observations. We extend this idea to higher dimensions by replacing the class of intervals by a general class of indexing sets, which specializes to the classes of ellipsoids, hyperrectangles or convex sets. The asymptotic behavior of our tolerance regions is derived using empirical process theory, in particular the concept of generalized quantiles. Finite sample properties of our tolerance regions are investigated through a simulation study. Real data examples are also presented

Status and Trend of the Main Allergenic Pollen Grains and Alternaria Spores in the City of Rome (2003-2019)

Today a large part of the European population is exposed to levels of air pollution exceeding the standards recommended by the World Health Organization. Moreover, air pollution and the seasonal emission of allergenic pollen are progressively affecting human health and can cause severe allergic reactions, particularly when air pollution combines with pollen allergen peaks. Unlike atmospheric pollutants of anthropogenic origin, pollen sources have a pulsating trend that leads to high values in the flowering period and values close to, or equal to, zero in the rest of the year. This aspect makes essential the definition of data coverage standards for the main allergenic taxa. For air quality assessment detailed classification criteria for monitoring stations are defined by international standards, not the same from the European Standards for the Sampling and analysis of airborne pollen grains and fungal spores. This paper describes the status and the air concentration trends of the main allergenic pollen and the Alternaria spore measured in Rome from 2003 to 2019 by the Aerobiological Monitoring Center of Tor Vergata (Rome) and calculated by the Seasonal Kendall test with the open-source OpenAir R package. The analysis was carried out on the daily concentrations of the most widespread allergenic taxa in Italy: Asteraceae, Betulaceae, Corylaceae, Cupressaceae/Taxaceae, Poaceae, Oleaceae, Urticaceae and the Alternaria spores