Tsallis statistics and gradually truncated Levy flight - distribution of an economical index

Tsallis postulated a generalized form for entropy and give rise to a new statistics now known as Tsallis statistics. In the present work, we compare the Tsallis statistics with the gradually truncated Levy flight, and discuss the distribution of an economical index-the Standard and Poor's 500-using the values of standard deviation as calculated by our model. We find that both statistics give almost the same distribution. Thus we feel that gradual truncation of Levy distribution, after certain critical step size for describing complex systems, is a requirement of generalized thermodynamics or similar. The gradually truncated Levy flight is based on physical considerations and bring a better physical picture of the dynamics of the whole system. Tsallis statistics gives a theoretical support. Both statistics together can be utilized for the development of a more exact portfolio theory or to understand better the complexities in human and financial behaviors. A comparison of both statistics is made. (C) 2002 Published by Elsevier B.V. B.V.

Size limiting in Tsallis statistics

Power law scaling is observed in many physical, biological and socio-economical complex systems and is now considered an important property of these systems. In general, power law exists in the central part of the distribution. It has deviations from power law for very small and very large variable sizes. Tsallis, through non-extensive thermodynamics, explained power law distribution in many cases including deviation from the power law. In case of very large steps, the used the heuristic crossover approach. In the present we present an alternative model in which we consider that the entropy factor 9 decreases with variable size due to the softening of long range interactions or memory. We apply this model for distribution of citation index of scientists and examination scores and are able to explain the distribution for entire variable range. In the present model, we can have very sharp cut-off without interfering with power law in its central part as observed in many cases. (C) 2008 Elsevier B.V. All rights reserved.

Assessment and statistics of Brazilian hydroelectric power plants: Dam areas versus installed and firm power

The Brazilian relief, predominantly composed by small mountains and plateaus, contributed to formation of rivers with high amount of falls. With exception to North-eastern Brazil, the climate of this country are rainy, which contributes to maintain water flows high. These elements are essential to a high hydroelectric potential, contributing to the choice of hydroelectric power plants as the main technology of electricity generation in Brazil. Though this is a renewable source, whose utilized resource is free, dams must to be established which generates a high environmental and social impact. The objective of this study is to evaluate the impact caused by these dams through the use of environmental indexes. These indexes are ratio formed by installed power with dam area of a hydro power plant, and ratio formed by firm power with this dam area. In this study, the greatest media values were found in South, Southeast, and Northeast regions respectively, and the smallest media values were found in North and Mid-West regions, respectively. The greatest encountered media indexes were also found in dams established in the 1950s. In the last six decades, the smallest indexes were registered by darns established in the 1980s. These indexes could be utilized as important instruments for environmental impact assessments, and could enable a dam to be established that depletes an ecosystem as less as possible.

Elicitation of multivariate prior distributions: A nonparametric Bayesian approach

In the context of Bayesian statistical analysis, elicitation is the process of formulating a prior density f(.) about one or more uncertain quantities to represent a person's knowledge and beliefs. Several different methods of eliciting prior distributions for one unknown parameter have been proposed. However, there are relatively few methods for specifying a multivariate prior distribution and most are just applicable to specific classes of problems and/or based on restrictive conditions, such as independence of variables. Besides, many of these procedures require the elicitation of variances and correlations, and sometimes elicitation of hyperparameters which are difficult for experts to specify in practice. Garthwaite et al. (2005) discuss the different methods proposed in the literature and the difficulties of eliciting multivariate prior distributions. We describe a flexible method of eliciting multivariate prior distributions applicable to a wide class of practical problems. Our approach does not assume a parametric form for the unknown prior density f(.), instead we use nonparametric Bayesian inference, modelling f(.) by a Gaussian process prior distribution. The expert is then asked to specify certain summaries of his/her distribution, such as the mean, mode, marginal quantiles and a small number of joint probabilities. The analyst receives that information, treating it as a data set D with which to update his/her prior beliefs to obtain the posterior distribution for f(.). Theoretical properties of joint and marginal priors are derived and numerical illustrations to demonstrate our approach are given. (C) 2010 Elsevier B.V. All rights reserved.

Geographic variation of Africanized honey bees (Apis mellifera L.) in Brazil: Multivariate morphometrics and racial admixture

The correspondence between morphometric and isozymic geographic variation patterns of Africanized honey bees in Brazil was analyzed. Morphometric data consisted of mean vectors of 19 wing traits measured in 42 local populations distributed throughout the country. Isozymic data refer to allelic frequencies of malate dehydrogenase (MDH), and were obtained from Lobo and Krieger. The two data sets were analyzed through canonical trend surface, principal components and spatial autocorrelation analyses, and showed north-south dines, demonstrating that Africanized honey bees in southern and southeastern Brazil are more similar to European honey bees than those found in northern and northeastern regions. Also, the morphometric variation is within the limits established by the racial admixture model, considering the expected values of Africanized honey bee fore wing length (WL) in southern and northeastern regions of Brazil, estimated by combining average values of WL in the three main subspecies involved in the Africanization process (Apis mellifera scutellata, A. m. ligustica and A. m. mellifera) with racial admixture coefficients.

Statistics on tropical convective storms observed by radar

Convective storm rainfall is of special importance to urban hydrological studies due to its temporal and spatial variability. Although dense networks of recording rain gauges can be employed to characterize such rainfall, very few investigations of this type have been undertaken due to their prohibitive cost. This paper reports some data on characteristics of tropical convective storms obtained from radar at Bauru in the State of São Paulo, Brazil. Periods of convective precipitation were identified by exclusion of those related to frontal activity with the help of synoptic maps and the radar screen record. The occurrence and evolution of convective storms were observed in two 28 km × 28 km windows obtaining information on the life history of convective cells and the magnitude of rainfall. Frequency distributions of the time of occurrence of convective rainfall, cell size, area covered, life duration and maximum and average rainfall observed in the experimental areas are presented and discussed.

Bayesian and multivariate methods applied to favorability quantification in recôncavo Basin and Ribeira Belt, Brazil

A methodology to define favorable areas in petroleum and mineral exploration is applied, which consists in weighting the exploratory variables, in order to characterize their importance as exploration guides. The exploration data are spatially integrated in the selected area to establish the association between variables and deposits, and the relationships among distribution, topology, and indicator pattern of all variables. Two methods of statistical analysis were compared. The first one is the Weights of Evidence Modeling, a conditional probability approach (Agterberg, 1989a), and the second one is the Principal Components Analysis (Pan, 1993). In the conditional method, the favorability estimation is based on the probability of deposit and variable joint occurrence, with the weights being defined as natural logarithms of likelihood ratios. In the multivariate analysis, the cells which contain deposits are selected as control cells and the weights are determined by eigendecomposition, being represented by the coefficients of the eigenvector related to the system's largest eigenvalue. The two techniques of weighting and complementary procedures were tested on two case studies: 1. Recôncavo Basin, Northeast Brazil (for Petroleum) and 2. Itaiacoca Formation of Ribeira Belt, Southeast Brazil (for Pb-Zn Mississippi Valley Type deposits). The applied methodology proved to be easy to use and of great assistance to predict the favorability in large areas, particularly in the initial phase of exploration programs. © 1998 International Association for Mathematical Geology.

Evaluation of the combined solar TiO2/photo-Fenton process using multivariate analysis

The effect of combining the photocatalytic processes using TiO 2 and the photo-Fenton reaction with Fe3+ or ferrioxalate as a source of Fe2+ was investigated in the degradation of 4-chlorophenol (4CP) and dichloroacetic acid (DCA) using solar irradiation. Multivariate analysis was used to evaluate the role of three variables: iron, H2O2 and TiO2 concentrations. The results show that TiO2 plays a minor role when compared to iron and H2O2 in the solar degradation of 4CP and DCA in the studied conditions. However, its presence can improve TOC removal when H2O2 is totally consumed. Iron and peroxide play major roles, especially when Fe(NO3)3 used in the degradation of 4CP. No significant synergistic effect was observed by the addition of TiO 2 in this process. On the other hand, synergistic effects were observed between FeOx and TiO2 and between H 2O2 and TiO2 in the degradation of DCA. © IWA Publishing 2004.

Progression of liver fibrosis in blood donors infected with hepatitis C virus

Background/Aims. Chronic hepatitis by HCV is progressive towards cirrhosis, with variable rate. We evaluated the rate of fibrosis progression (RFP), risk factors associated with advanced fibrosis (F3 and F4), and estimated the evolution time to cirrhosis. Methods. We transversely selected 142 blood donors infected only with HCV, with a known route of infection, submitted to liver biopsy at admission. RFP= ratio between stage of fibrosis (METAVIR)/estimated duration of infection in years. Non-parametric tests and logistic regression analysis, with significance level of 5% were used. Results. Median RFP was 0.086 U/year (0.05 - 0.142). Ten patients had F4 and 25 had F3. Median RFP values were significantly different (p=0.001) from one age group at contamination to the others and ALT and AST levels. There were no differences in the expected evolution to cirrhosis between intermediate fibrosers (F2) and the rapid fibrosers (F3 and F4). The independent variables associated with advanced fibrosis were ALT (OR 7.2) and GGT (OR 6.4) and age at inclusion (OR 1.12). Conclusion. This study suggests that RFP is extremely variable, it is exponential with age, and mainly influenced by host characteristics, especially age at contamination and possibly ethnical group. These asymptomatic patients had high percentage of fibrosis F2, F3 and F4.

HPLC determination of hemoglobins to establish reference values with the aid of statistics and informatics

The purpose of the present study was to establish reference values for hemoglobins (Hb) using HPLC, in samples containing normal Hb (AA), sickle cell trait without alpha-thalassemia (AS), sickle cell trait with alpha-thalassemia (ASH), sickle cell anemia (SS), and Hb SC disease (SC). The blood samples were analyzed by electrophoresis, HPLC and molecular procedures. The Hb A2 mean was 4.30 ± 0.44% in AS, 4.18 ± 0.42% in ASH, 3.90 ± 1.14% in SS, and 4.39 ± 0.35% in SC. They were similar, but above the normal range. Between the AS and ASH groups, only the amount of Hb S was higher in the AS group. The Hb S mean in the AS group was 38.54 ± 3.01% and in the ASH it was 36.54 ± 3.76%. In the qualitative analysis, using FastMap, distinct groups were seen: AA and SS located at opposite extremes, AS and ASH with overlapping values and intermediate distribution, SC between heterozygotes and the SS group. Hb S was confirmed by allele-specific polymerase chain reaction. The Hb values established will be available for use as a reference for the Brazilian population, drawing attention to the increased levels of Hb A2, which should be considered with caution to prevent incorrect diagnoses. ©FUNPEC-RP.

The use of principal components and univariate charts to control multivariate processes

In this article, we evaluate the performance of the T2 chart based on the principal components (PC chart) and the simultaneous univariate control charts based on the original variables (SU X̄ charts) or based on the principal components (SUPC charts). The main reason to consider the PC chart lies on the dimensionality reduction. However, depending on the disturbance and on the way the original variables are related, the chart is very slow in signaling, except when all variables are negatively correlated and the principal component is wisely selected. Comparing the SU X̄, the SUPC and the T 2 charts we conclude that the SU X̄ charts (SUPC charts) have a better overall performance when the variables are positively (negatively) correlated. We also develop the expression to obtain the power of two S 2 charts designed for monitoring the covariance matrix. These joint S2 charts are, in the majority of the cases, more efficient than the generalized variance |S| chart.

Monitoring bivariate processes

The T2 chart and the generalized variance |S| chart are the usual tools for monitoring the mean vector and the covariance matrix of multivariate processes. The main drawback of these charts is the difficulty to obtain and to interpret the values of their monitoring statistics. In this paper, we study control charts for monitoring bivariate processes that only requires the computation of sample means (the ZMAX chart) for monitoring the mean vector, sample variances (the VMAX chart) for monitoring the covariance matrix, or both sample means and sample variances (the MCMAX chart) in the case of the joint control of the mean vector and the covariance matrix.

ECLAC Development of official statistics in the region. Report of the Economic Commission for Latin America and the Caribbean on the development of official statistics in Latin America and the Caribbean

This document was prepared by the Economic Commission for Latin America and the Caribbean (ECLAC); and offers a description of the main trends in the development of official statistics in Latin America and the Caribbean and the principal challenges in that regard.The first chapter provides an analysis of the state of development of statistical production in the region, based on statistical information for 41 Latin American and Caribbean countries and eight specific areas. The institutional organization of national statistical systems in the region is also described. Chapter II examines the history and current status of mechanisms for regional and subregional coordination and of the Statistical Conference of the Americas of ECLAC. Chapter III describes the main challenges for official statistics in the countries of the region and the strategies that the Statistical Conference of the Americas and ECLAC propose to implement in order to address them.