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Empirical Fit (empirical + fit)
Selected AbstractsGeneralized Birnbaum-Saunders distributions applied to air pollutant concentrationENVIRONMETRICS, Issue 3 2008Víctor Leiva Abstract The generalized Birnbaum-Saunders (GBS) distribution is a new class of positively skewed models with lighter and heavier tails than the traditional Birnbaum-Saunders (BS) distribution, which is largely applied to study lifetimes. However, the theoretical argument and the interesting properties of the GBS model have made its application possible beyond the lifetime analysis. The aim of this paper is to present the GBS distribution as a useful model for describing pollution data and deriving its positive and negative moments. Based on these moments, we develop estimation and goodness-of-fit methods. Also, some properties of the proposed estimators useful for developing asymptotic inference are presented. Finally, an application with real data from Environmental Sciences is given to illustrate the methodology developed. This example shows that the empirical fit of the GBS distribution to the data is very good. Thus, the GBS model is appropriate for describing air pollutant concentration data, which produces better results than the lognormal model when the administrative target is determined for abating air pollution. Copyright © 2007 John Wiley & Sons, Ltd. [source] Br/Cl signature of hydrothermal fluids: liquid,vapour fractionation of bromine revisitedGEOFLUIDS (ELECTRONIC), Issue 2 2006A. LIEBSCHER Abstract Br/Cl ratios of hydrothermal fluids are widely used as geochemical tracers in marine hydrothermal systems to prove fluid phase separation processes. However, previous results of the liquid,vapour fractionation of bromine are ambiguous. Here we report new experimental results of the liquid,vapour fractionation of bromine in the system H2O,NaCl,NaBr at 380,450°C and 22.9,41.7 MPa. Our data indicate that bromine is generally more enriched than chlorine in the liquid phase. Calculated exchange coefficients KD(Br-Cl)liquid-vapour for the reaction Brvapour + Clliquid = Brliquid + Clvapour are between 0.94 ± 0.08 and 1.66 ± 0.14 within the investigated P,T range. They correlate positively with DClliquid-vapour and suggest increasing bromine,chlorine fractionation with increasing opening of the liquid,vapour solvus, i.e. increasing distance to the critical curve in the H2O,NaCl system. An empirical fit of the form KD(Br-Cl)liquid-vapour = a*ln[b*(DClliquid-vapour,1) + e1/a] yields a = 0.349 and b = 1.697. Based on this empirical fit and the well-constrained phase relations in the H2O,NaCl system we calculated the effect of fluid phase separation on the Br/Cl signature of a hydrothermal fluid with initial seawater composition for closed and open adiabatic ascents along the 4.5 and 4.8 J g,1 K,1 isentropes. The calculations indicate that fluid phase separation can significantly alter the Br/Cl ratio in hydrothermal fluids. The predicted Br/Cl evolutions are in accord with the Br/Cl signatures in low-salinity vent fluids from the 9 to 10°N East Pacific Rise. [source] Empirical assessment of a collaborative filtering algorithm based on OWA operatorsINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 12 2008Miguel-Angel Sicilia Classical collaborative filtering algorithms generate recommendations on the basis of ratings provided by users that express their subjective preference on concrete items. The correlation of ratings is used in such schemes as an implicit measure of common interest between users, that is used to predict ratings, so that these ratings determine recommendations. The common formulae used for the computation of predicted ratings use standard weighted averaging schemes as the fixed aggregation mechanism that determines the result of the prediction. Nonetheless, the surrounding context of these rating systems suggest that an approach considering a degree of group consensus in the aggregation process may better capture the essence of the "word,of,mouth" philosophy of such systems. This paper reports on the empirical evaluation of such an alternative approach in which OWA operators with different properties are tested against a dataset to search for the better empirical adjustment. The resulting algorithm can be considered as a generalization of the original Pearson formula based algorithm that allows for the fitting of the aggregation behavior to concrete databases of ratings. The results show that for the particular context studied, higher orness degrees reduce overall error measures, especially for high ratings, which are more relevant in recommendation settings. The adjustment procedure can be used as a general-purpose method for the empirical fit of the behavior of collaborative filtering systems. © 2008 Wiley Periodicals, Inc. [source] Reconsideration of the physical and empirical origins of Z,R relations in radar meteorologyTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 572 2001A. R. Jameson Abstract The rainfall rate, R, and the radar reflectivity factor, Z, are represented by a sum over a finite number of raindrops. It is shown here and in past work that these variables should be linearly related. Yet observations show that correlations between R and Z are often more appropriately described by nonlinear power laws. In the absence of measurement effects, why should this be so? In order to justify this observation, there have been many attempts to create physical ,explanations' for power laws. However, the present work argues that, because correlations do not prove causation (an accepted fact in the statistical sciences), such explanations are suspect, particularly since the parametric fits are not unique and because they exhibit fundamental physical inconsistencies. So why, then, do so many correlations fit power laws when physical arguments show that Z and R should be related linearly? It is shown in the present work that physically based, linear, relations between Z and R apply in statistically homogeneous rain. (Note that statistical homogeneity does not mean that the rain is spatially uniform.) In contrast, nonlinear power laws are empirical fits to correlated, but statistically inhomogeneous data. This conclusion is proven theoretically after developing a ,generalized' Z,R relation based upon physical consideration of R and Z as random variables. This relation explicitly incorporates details of the drop microphysics as well as the variability in measurements of Z and R. In statistically homogeneous rain, this generalized expression shows that the coefficient relating Z and R is a constant resulting in a linear Z,R relation. In statistically inhomogeneous rain, however, the coefficient varies in an unknown fashion so that one must resort to statistical fits, often power laws, in order to relate the two quantities empirically over widely varying conditions. This conclusion is independently verified using Monte Carlo simulations of rain from earlier work and is also corroborated using disdrometer observations. Thus, the justification for nonlinear power-law Z,R relations is not physical, but rather statistical, in that they provide convenient parametric fits for estimating mean R from measured mean Z in statistically inhomogeneous rain. Finally, examples based upon disdrometer data suggest that such generalized relations between two variables defined by such sums are potentially useful over a wide range of remote-sensing problems and over a wide range of scales. The examples also offer hope that data collected over disparate sampling-volumes and sampling-frequencies can still be combined to yield meaningful estimates. Although additional testing is required, this allows us to write programs which combine estimates of R using remote-sensing techniques with sparse but direct rainfall observations. [source] | ||||||||||