The statistical properties of tropical ice clouds generated by the West-African and Australian monsoons from ground-based radar-lidar observations

In the present paper we characterize the statistical properties of non-precipitating tropical ice clouds (deep ice anvils resulting from deep convection and cirrus clouds) over Niamey, Niger, West Africa, and Darwin, northern Australia, using ground-based radar–lidar observations from the Atmospheric Radiation Measurement (ARM) programme. The ice cloud properties analysed in this paper are the frequency of ice cloud occurrence, cloud fraction, the morphological properties (cloud-top height, base height, and thickness), the microphysical and radiative properties (ice water content, visible extinction, effective radius, terminal fall speed, and concentration), and the internal cloud dynamics (in-cloud vertical air velocity). The main highlight of the paper is that it characterizes for the first time the probability density functions of the tropical ice cloud properties, their vertical variability and their diurnal variability at the same time. This is particularly important over West Africa, since the ARM deployment in Niamey provides the first vertically resolved observations of non-precipitating ice clouds in this crucial area in terms of redistribution of water and energy in the troposphere. The comparison between the two sites also provides an additional observational basis for the evaluation of the parametrization of clouds in large-scale models, which should be able to reproduce both the statistical properties at each site and the differences between the two sites. The frequency of ice cloud occurrence is found to be much larger over Darwin when compared to Niamey, and with a much larger diurnal variability, which is well correlated with the diurnal cycle of deep convective activity. The diurnal cycle of the ice cloud occurrence over Niamey is also much less correlated with that of deep convective activity than over Darwin, probably owing to the fact that Niamey is further away from the deep convective sources of the region. The frequency distributions of cloud fraction are strongly bimodal and broadly similar over the two sites, with a predominance of clouds characterized either by a very small cloud fraction (less than 0.3) or a very large cloud fraction (larger than 0.9). The ice clouds over Darwin are also much thicker (by 1 km or more statistically) and are characterized by a much larger diurnal variability than ice clouds over Niamey. Ice clouds over Niamey are also characterized by smaller particle sizes and fall speeds but in much larger concentrations, thereby carrying more ice water and producing more visible extinction than the ice clouds over Darwin. It is also found that there is a much larger occurrence of downward in-cloud air motions less than 1 m s−1 over Darwin, which together with the larger fall speeds retrieved over Darwin indicates that the life cycle of ice clouds is probably shorter over Darwin than over Niamey.

A statistical model for sea surface diurnal warming driven by numercial weather predictions fluxes and winds

A statistical model is derived relating the diurnal variation of sea surface temperature (SST) to the net surface heat flux and surface wind speed from a numerical weather prediction (NWP) model. The model is derived using fluxes and winds from the European Centre for Medium-Range Weather Forecasting (ECMWF) NWP model and SSTs from the Spinning Enhanced Visible and Infrared Imager (SEVIRI). In the model, diurnal warming has a linear dependence on the net surface heat flux integrated since (approximately) dawn and an inverse quadratic dependence on the maximum of the surface wind speed in the same period. The model coefficients are found by matching, for a given integrated heat flux, the frequency distributions of the maximum wind speed and the observed warming. Diurnal cooling, where it occurs, is modelled as proportional to the integrated heat flux divided by the heat capacity of the seasonal mixed layer. The model reproduces the statistics (mean, standard deviation, and 95-percentile) of the diurnal variation of SST seen by SEVIRI and reproduces the geographical pattern of mean warming seen by the Advanced Microwave Scanning Radiometer (AMSR-E). We use the functional dependencies in the statistical model to test the behaviour of two physical model of diurnal warming that display contrasting systematic errors.

The DYMECS project: a statistical approach for the evaluation of convective storms in high-resolution NWP models

A new frontier in weather forecasting is emerging by operational forecast models now being run at convection-permitting resolutions at many national weather services. However, this is not a panacea; significant systematic errors remain in the character of convective storms and rainfall distributions. The DYMECS project (Dynamical and Microphysical Evolution of Convective Storms) is taking a fundamentally new approach to evaluate and improve such models: rather than relying on a limited number of cases, which may not be representative, we have gathered a large database of 3D storm structures on 40 convective days using the Chilbolton radar in southern England. We have related these structures to storm life-cycles derived by tracking features in the rainfall from the UK radar network, and compared them statistically to storm structures in the Met Office model, which we ran at horizontal grid length between 1.5 km and 100 m, including simulations with different subgrid mixing length. We also evaluated the scale and intensity of convective updrafts using a new radar technique. We find that the horizontal size of simulated convective storms and the updrafts within them is much too large at 1.5-km resolution, such that the convective mass flux of individual updrafts can be too large by an order of magnitude. The scale of precipitation cores and updrafts decreases steadily with decreasing grid lengths, as does the typical storm lifetime. The 200-m grid-length simulation with standard mixing length performs best over all diagnostics, although a greater mixing length improves the representation of deep convective storms.

Mapping power law distributions in digital health social networks: methods, interpretations, and practical implications

BACKGROUND: Social networks are common in digital health. A new stream of research is beginning to investigate the mechanisms of digital health social networks (DHSNs), how they are structured, how they function, and how their growth can be nurtured and managed. DHSNs increase in value when additional content is added, and the structure of networks may resemble the characteristics of power laws. Power laws are contrary to traditional Gaussian averages in that they demonstrate correlated phenomena. OBJECTIVES: The objective of this study is to investigate whether the distribution frequency in four DHSNs can be characterized as following a power law. A second objective is to describe the method used to determine the comparison. METHODS: Data from four DHSNs—Alcohol Help Center (AHC), Depression Center (DC), Panic Center (PC), and Stop Smoking Center (SSC)—were compared to power law distributions. To assist future researchers and managers, the 5-step methodology used to analyze and compare datasets is described. RESULTS: All four DHSNs were found to have right-skewed distributions, indicating the data were not normally distributed. When power trend lines were added to each frequency distribution, R(2) values indicated that, to a very high degree, the variance in post frequencies can be explained by actor rank (AHC .962, DC .975, PC .969, SSC .95). Spearman correlations provided further indication of the strength and statistical significance of the relationship (AHC .987. DC .967, PC .983, SSC .993, P<.001). CONCLUSIONS: This is the first study to investigate power distributions across multiple DHSNs, each addressing a unique condition. Results indicate that despite vast differences in theme, content, and length of existence, DHSNs follow properties of power laws. The structure of DHSNs is important as it gives insight to researchers and managers into the nature and mechanisms of network functionality. The 5-step process undertaken to compare actor contribution patterns can be replicated in networks that are managed by other organizations, and we conjecture that patterns observed in this study could be found in other DHSNs. Future research should analyze network growth over time and examine the characteristics and survival rates of superusers.

A new family of generalized distributions

Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 462 (1980), pp. 79-88] introduced a distribution for double-bounded random processes with hydrological applications. For the first time, based on this distribution, we describe a new family of generalized distributions (denoted with the prefix `Kw`) to extend the normal, Weibull, gamma, Gumbel, inverse Gaussian distributions, among several well-known distributions. Some special distributions in the new family such as the Kw-normal, Kw-Weibull, Kw-gamma, Kw-Gumbel and Kw-inverse Gaussian distribution are discussed. We express the ordinary moments of any Kw generalized distribution as linear functions of probability weighted moments (PWMs) of the parent distribution. We also obtain the ordinary moments of order statistics as functions of PWMs of the baseline distribution. We use the method of maximum likelihood to fit the distributions in the new class and illustrate the potentiality of the new model with an application to real data.

Robust linear mixed models with skew-normal independent distributions from a Bayesian perspective

Linear mixed models were developed to handle clustered data and have been a topic of increasing interest in statistics for the past 50 years. Generally. the normality (or symmetry) of the random effects is a common assumption in linear mixed models but it may, sometimes, be unrealistic, obscuring important features of among-subjects variation. In this article, we utilize skew-normal/independent distributions as a tool for robust modeling of linear mixed models under a Bayesian paradigm. The skew-normal/independent distributions is an attractive class of asymmetric heavy-tailed distributions that includes the skew-normal distribution, skew-t, skew-slash and the skew-contaminated normal distributions as special cases, providing an appealing robust alternative to the routine use of symmetric distributions in this type of models. The methods developed are illustrated using a real data set from Framingham cholesterol study. (C) 2009 Elsevier B.V. All rights reserved.

Inflated beta distributions

This paper considers the issue of modeling fractional data observed on [0,1), (0,1] or [0,1]. Mixed continuous-discrete distributions are proposed. The beta distribution is used to describe the continuous component of the model since its density can have quite different shapes depending on the values of the two parameters that index the distribution. Properties of the proposed distributions are examined. Also, estimation based on maximum likelihood and conditional moments is discussed. Finally, practical applications that employ real data are presented.

An R implementation for generalized Birnbaum-Saunders distributions

The Birnbaum-Saunders (BS) model is a positively skewed statistical distribution that has received great attention in recent decades. A generalized version of this model was derived based on symmetrical distributions in the real line named the generalized BS (GBS) distribution. The R package named gbs was developed to analyze data from GBS models. This package contains probabilistic and reliability indicators and random number generators from GBS distributions. Parameter estimates for censored and uncensored data can also be obtained by means of likelihood methods from the gbs package. Goodness-of-fit and diagnostic methods were also implemented in this package in order to check the suitability of the GBS models. in this article, the capabilities and features of the gbs package are illustrated by using simulated and real data sets. Shape and reliability analyses for GBS models are presented. A simulation study for evaluating the quality and sensitivity of the estimation method developed in the package is provided and discussed. (C) 2008 Elsevier B.V. All rights reserved.

A fast and robust statistical test based on likelihood ratio with Bartlett correction to identify Granger causality between gene sets

We propose a likelihood ratio test ( LRT) with Bartlett correction in order to identify Granger causality between sets of time series gene expression data. The performance of the proposed test is compared to a previously published bootstrapbased approach. LRT is shown to be significantly faster and statistically powerful even within non- Normal distributions. An R package named gGranger containing an implementation for both Granger causality identification tests is also provided.

Factors affecting the technical efficiency of production of the Brazilian banking system : a comparison of four statistical models in the context of data envelopment analysis

This paper uses an output oriented Data Envelopment Analysis (DEA) measure of technical efficiency to assess the technical efficiencies of the Brazilian banking system. Four approaches to estimation are compared in order to assess the significance of factors affecting inefficiency. These are nonparametric Analysis of Covariance, maximum likelihood using a family of exponential distributions, maximum likelihood using a family of truncated normal distributions, and the normal Tobit model. The sole focus of the paper is on a combined measure of output and the data analyzed refers to the year 2001. The factors of interest in the analysis and likely to affect efficiency are bank nature (multiple and commercial), bank type (credit, business, bursary and retail), bank size (large, medium, small and micro), bank control (private and public), bank origin (domestic and foreign), and non-performing loans. The latter is a measure of bank risk. All quantitative variables, including non-performing loans, are measured on a per employee basis. The best fits to the data are provided by the exponential family and the nonparametric Analysis of Covariance. The significance of a factor however varies according to the model fit although it can be said that there is some agreements between the best models. A highly significant association in all models fitted is observed only for nonperforming loans. The nonparametric Analysis of Covariance is more consistent with the inefficiency median responses observed for the qualitative factors. The findings of the analysis reinforce the significant association of the level of bank inefficiency, measured by DEA residuals, with the risk of bank failure.

Statistical modelling of extreme rainfall in Madeira Island

Extreme rainfall events have triggered a significant number of flash floods in Madeira Island along its past and recent history. Madeira is a volcanic island where the spatial rainfall distribution is strongly affected by its rugged topography. In this thesis, annual maximum of daily rainfall data from 25 rain gauge stations located in Madeira Island were modelled by the generalised extreme value distribution. Also, the hypothesis of a Gumbel distribution was tested by two methods and the existence of a linear trend in both distributions parameters was analysed. Estimates for the 50– and 100–year return levels were also obtained. Still in an univariate context, the assumption that a distribution function belongs to the domain of attraction of an extreme value distribution for monthly maximum rainfall data was tested for the rainy season. The available data was then analysed in order to find the most suitable domain of attraction for the sampled distribution. In a different approach, a search for thresholds was also performed for daily rainfall values through a graphical analysis. In a multivariate context, a study was made on the dependence between extreme rainfall values from the considered stations based on Kendall’s τ measure. This study suggests the influence of factors such as altitude, slope orientation, distance between stations and their proximity of the sea on the spatial distribution of extreme rainfall. Groups of three pairwise associated stations were also obtained and an adjustment was made to a family of extreme value copulas involving the Marshall–Olkin family, whose parameters can be written as a function of Kendall’s τ association measures of the obtained pairs.

Nucleon flavor asymmetry in a statistical quark model

A statistical model of linear-confined quarks is applied to obtain the flavor asymmetry of the nucleon sea. The model parametrization is fixed by the experimental available data, where a temperature parameter is used to fit the Gottfried sum rule violation. Results are presented for the ratios of light quark and antiquark distributions, d/u and (d) over bar/(u) over bar.

Microscopic origin of non-Gaussian distributions of financial returns

In this paper we study the possible microscopic origin of heavy-tailed probability density distributions for the price variation of financial instruments. We extend the standard log-normal process to include another random component in the so-called stochastic volatility models. We study these models under an assumption, akin to the Born-Oppenheimer approximation, in which the volatility has already relaxed to its equilibrium distribution and acts as a background to the evolution of the price process. In this approximation, we show that all models of stochastic volatility should exhibit a scaling relation in the time lag of zero-drift modified log-returns. We verify that the Dow-Jones Industrial Average index indeed follows this scaling. We then focus on two popular stochastic volatility models, the Heston and Hull-White models. In particular, we show that in the Hull-White model the resulting probability distribution of log-returns in this approximation corresponds to the Tsallis (t-Student) distribution. The Tsallis parameters are given in terms of the microscopic stochastic volatility model. Finally, we show that the log-returns for 30 years Dow Jones index data is well fitted by a Tsallis distribution, obtaining the relevant parameters. (c) 2007 Elsevier B.V. All rights reserved.

Quark sea structure functions of the nucleon in a statistical model

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Power-law distributions for the citation index of scientific publications and scientists

The number of citations of a scientific publication or of an individual scientist has become an important factor of quality assessment in science. We report a study of the statistical distribution of the citation index of both scientific publications and scientists. We give numerical evidence that Tsallis (power law) statistics explains the entire distribution over eight orders of magnitude (10-4 to 10(4)). Also, we draw Zipf plots in order to analyze the statistical distribution of the citation index of Brazilian and international physicists and chemists. The relatively small group of Brazilian scientists seems more adequate to explain the dynamics of the citation index. In this case, we find that the distribution of the citation index can also be explained by a gradually truncated power law with similar parameters. We finally discuss possible mechanisms behind the citation index of scientists and scientific publications.