scholarly journals Fractional calculus approach to the statistical characterization of random variables and vectors

2010 ◽  
Vol 389 (5) ◽  
pp. 909-920 ◽  
Author(s):  
Giulio Cottone ◽  
Mario Di Paola ◽  
Ralf Metzler
Author(s):  
Saverio Perri ◽  
Amilcare Porporato

Abstract Human-induced environmental change increasingly threatens the stability of socio-ecological systems. Careful statistical characterization of environmental concentrations is critical to quantify and predict the consequences of such changes on human and ecosystems conditions. However, while concentrations are naturally defined as the ratio between solute mass and solvent volume, they have rarely been treated as such, typically limiting the analysis to familiar distributions generically used for any other environmental variable. To address this gap, we propose a more general framework that leverages their definition explicitly as ratios of random variables. We show that the resulting models accurately describe the behavior of nitrate plus nitrite in US rivers and salt concentration in estuaries in the Everglades by accounting for heavy tails potentially emerging when the water volume fluctuates around low values. Models that preclude the presence of heavy tails and the related high probability of extreme concentrations could significantly undermine the accuracy of diagnostic frameworks and the effectiveness of mitigation interventions, especially for soil contamination characterized by a water volume (i.e., soil moisture) frequently approaching zero.


Energies ◽  
2021 ◽  
Vol 14 (3) ◽  
pp. 759
Author(s):  
Andrea Mariscotti

Accurate and comprehensive methods for the assessment of radiated electromagnetic emissions in modern electric transportation systems are a necessity. The characteristics and susceptibility of modern victim signaling and communication radio services, operating within and outside the right-of-way, require an update of the measurement methods integrating or replacing the swept frequency technique with time domain approaches. Applicable standards are the EN 50121 (equivalent to the IEC 62236) and Urban Mass Transport Association (UMTA) with additional specifications from project contracts. This work discusses the standardized methods and settings, and the representative operating conditions, highlighting areas where improvements are possible and opportune (statistical characterization of measurement results, identification and distinction of emissions and line resonances, and narrowband and broadband phenomena). In particular for the Electromagnetic Compatibility (EMC) assessment with new Digital Communication Systems, the characterization of time distribution of spectral properties is discussed, e.g., by means of Amplitude Probability Distribution and including time distribution information. The problem of determination of site and setup uncertainty and repeatability is also discussed, observing on one hand the lack of clear indications in standards and, on the other hand, the non-ideality and intrinsic variability of measurement conditions (e.g., rolling stock operating conditions, synchronization issues, and electric arc intermittence).


GPS Solutions ◽  
2021 ◽  
Vol 25 (3) ◽  
Author(s):  
Guo Chen ◽  
Renyu Zhou ◽  
Zhigang Hu ◽  
Yifei Lv ◽  
Na Wei ◽  
...  

2010 ◽  
Vol 88 (1) ◽  
pp. 93-102 ◽  
Author(s):  
MARGARYTA MYRONYUK

AbstractLet X be a countable discrete abelian group with automorphism group Aut(X). Let ξ1 and ξ2 be independent X-valued random variables with distributions μ1 and μ2, respectively. Suppose that α1,α2,β1,β2∈Aut(X) and β1α−11±β2α−12∈Aut(X). Assuming that the conditional distribution of the linear form L2 given L1 is symmetric, where L2=β1ξ1+β2ξ2 and L1=α1ξ1+α2ξ2, we describe all possibilities for the μj. This is a group-theoretic analogue of Heyde’s characterization of Gaussian distributions on the real line.


2010 ◽  
Author(s):  
David Levitz ◽  
Ardalan Ardeshiri ◽  
Jabeer Ahmed ◽  
Daniel S. Gareau ◽  
Steven L. Jacques

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