Constructing the frequency and wave normal distribution of whistler-mode wave power

We introduce a new methodology that allows the construction of wave frequency distributions due to growing incoherent whistler-mode waves in the magnetosphere. The technique combines the equations of geometric optics (i.e. raytracing) with the equation of transfer of radiation in an anisotropic lossy medium to obtain spectral energy density as a function of frequency and wavenormal angle. We describe the method in detail, and then demonstrate how it could be used in an idealised magnetosphere during quiet geomagnetic conditions. For a specific set of plasma conditions, we predict that the wave power peaks off the equator at ~15 degrees magnetic latitude. The new calculations predict that wave power as a function of frequency can be adequately described using a Gaussian function, but as a function of wavenormal angle, it more closely resembles a skew normal distribution. The technique described in this paper is the first known estimate of the parallel and oblique incoherent wave spectrum as a result of growing whistler-mode waves, and provides a means to incorporate self-consistent wave-particle interactions in a kinetic model of the magnetosphere over a large volume.

Non-Maxwellian ion velocity distributions observed using EISCAT

Recent observations from the EISCAT incoherent scatter radar have revealed bursts of poleward ion flow in the dayside auroral ionosphere which are consistent with the ionospheric signature of flux transfer events at the magnetopause. These bursts frequently contain ion drifts which exceed the neutral thermal speed and, because the neutral thermospheric wind is incapable of responding sufficiently rapidly, toroidal, non-Maxwellian ion velocity distributions are expected. The EISCAT observations are made with high time resolution (15 seconds) and at a large angle to the geomagnetic field (73.5°), allowing the non-Maxwellian nature of the distribution to be observed remotely for the first time. The observed features are also strongly suggestive of a toroidal distribution: characteristic spectral shape, increased scattered power (both consistent with reduced Landau damping and enhanced electric field fluctuations) and excessively high line-of-sight ion temperatures deduced if a Maxwellian distribution is assumed. These remote sensing observations allow the evolution of the distributions to be observed. They are found to be non-Maxwellian whenever the ion drift exceeds the neutral thermal speed, indicating that such distributions can exist over the time scale of the flow burst events (several minutes).

The complementary exponential power lifetime model

In this paper we propose a new lifetime distribution which can handle bathtub-shaped unimodal increasing and decreasing hazard rate functions The model has three parameters and generalizes the exponential power distribution proposed by Smith and Bain (1975) with the inclusion of an additional shape parameter The maximum likelihood estimation procedure is discussed A small-scale simulation study examines the performance of the likelihood ratio statistics under small and moderate sized samples Three real datasets Illustrate the methodology (C) 2010 Elsevier B V All rights reserved

Power series generalized nonlinear models

We introduce in this paper a new class of discrete generalized nonlinear models to extend the binomial, Poisson and negative binomial models to cope with count data. This class of models includes some important models such as log-nonlinear models, logit, probit and negative binomial nonlinear models, generalized Poisson and generalized negative binomial regression models, among other models, which enables the fitting of a wide range of models to count data. We derive an iterative process for fitting these models by maximum likelihood and discuss inference on the parameters. The usefulness of the new class of models is illustrated with an application to a real data set. (C) 2008 Elsevier B.V. All rights reserved.

Size and power properties of some tests in the Birnbaum-Saunders regression model

The Birnbaum-Saunders distribution has been used quite effectively to model times to failure for materials subject to fatigue and for modeling lifetime data. In this paper we obtain asymptotic expansions, up to order n(-1/2) and under a sequence of Pitman alternatives, for the non-null distribution functions of the likelihood ratio, Wald, score and gradient test statistics in the Birnbaum-Saunders regression model. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the shape parameter. Monte Carlo simulation is presented in order to compare the finite-sample performance of these tests. We also present two empirical applications. (C) 2010 Elsevier B.V. All rights reserved.

Properties and Inference on the Skew-Curved-Symmetric Family of Distributions

In this article, we study some results related to a specific class of distributions, called skew-curved-symmetric family of distributions that depends on a parameter controlling the skewness and kurtosis at the same time. Special elements of this family which are studied include symmetric and well-known asymmetric distributions. General results are given for the score function and the observed information matrix. It is shown that the observed information matrix is always singular for some special cases. We illustrate the flexibility of this class of distributions with an application to a real dataset on characteristics of Australian athletes.

Local power of some tests in exponential family nonlinear models

In this paper we obtain asymptotic expansions up to order n(-1/2) for the nonnull distribution functions of the likelihood ratio, Wald, score and gradient test statistics in exponential family nonlinear models (Cordeiro and Paula, 1989), under a sequence of Pitman alternatives. The asymptotic distributions of all four statistics are obtained for testing a subset of regression parameters and for testing the dispersion parameter, thus generalising the results given in Cordeiro et al. (1994) and Ferrari et al. (1997). We also present Monte Carlo simulations in order to compare the finite-sample performance of these tests. (C) 2010 Elsevier B.V. All rights reserved.

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.

Size distributions of fine silicate and other particles in Masaya's volcanic plume

Direct-sampling and remote-sensing measurements were made at the crater rim of Masaya volcano (Nicaragua) to sample the aerosol plume emanating from the active vent. We report the first measurements of the size distribution of fine silicate particles (d <10 mu m) in Masaya's plume, by automated scanning electron microscopy (QEMSCAN) analysis of a particle filter. The particle size distribution was approximately lognormal with modal d similar to 1.15 mu m. The majority of these particles were found to be spherical. These particles are interpreted to be droplets of quenched magma produced by a spattering process. Compositional analyses confirm earlier reports that the fine silicate particles show a range of compositions between that of the degassing magma and nearly pure silica and that the extent of compositional variability decreases with increasing particle size. These results indicate that fine silicate particles are altered owing to reactions with acidic droplets in the plume. The emission flux of fine silicate particles was estimated as similar to 10(11) s(-1), equivalent to similar to 55 kg d(-1). Sun photometry, aerosol spectrometry, and thermal precipitation were used to determine the overall particle size distribution of the plume (0.01 < d(mu m) < 10). Sun photometry and aerosol spectrometry measurements indicate the presence of a large number of particles (assumed to be aqueous) with d similar to 1 mu m. Aerosol spectrometry measurements further show an increase in particle size as the nighttime approached. The emission flux of particles from Masaya was estimated as similar to 10(17) s(-1), equivalent to similar to 5.5 Mg d(-1) where d < 4 mu m.

Composition-resolved size distributions of volcanic aerosols in the Mt. Etna plumes

Particle size distributions for soluble and insoluble species in Mt. Etna's summit plumes were measured across an extended size range (10 nm < d < 100 mu m) using a combination of techniques. Automated scanning electron microscopy (QEMSCAN) was used to chemically analyze many thousands of insoluble particles (collected on pumped filters) allowing the relationships between particle size, shape, and composition to be investigated. The size distribution of fine silicate particles (d < 10 mu m) was found to be lognormal, consistent with formation by bursting of gas bubbles at the surface of the magma. The compositions of fine silicate particles were found to vary between magmatic and nearly pure silica; this is consistent with depletion of metal ions by reactions in the acidic environment of the gas plume and vent. Measurements of the size, shape and composition of fine silicate particles may potentially offer insights into preemission, synemission, and postemission processes. The mass flux of fine silicate particles from Mt. Etna released during noneruptive volcanic degassing in 2004 and 2005 was estimated to be similar to 7000 kg d(-1). Analysis of particles in the range 0.1 < d/mu m < 100 by ion chromatography shows that there are persistent differences in the size distributions of sulfate aerosols between the two main summit plumes. Analysis of particles in the range 0.01 mu m < d < 0.1 mu m by scanning transmission electron microscopy (STEM) shows that there are significant levels of nanoparticles in the Mt. Etna plumes although their compositions remain uncertain.

Power law distribution in education: Effect of economical, teaching, and study conditions in university entrance examination

We studied the statistical distribution of student's performance, which is measured through their marks, in university entrance examination (Vestibular) of UNESP (Universidade Estadual Paulista) with respect to (i) period of study - day versus night period (ii) teaching conditions - private versus public school (iii) economical conditions - high versus low family income. We observed long ubiquitous power law tails in physical and biological sciences in all cases. The mean value increases with better study conditions followed by better teaching and economical conditions. In humanities, the distribution is close to normal distribution with very small tail. This indicates that these power law tails in science subjects axe due to the nature of the subjects themselves. Further and better study, teaching and economical conditions axe more important for physical and biological sciences in comparison to humanities at this level of study. We explain these statistical distributions through Gradually Truncated Power law distributions. We discuss the possible reason for this peculiar behavior.

Analytical and Monte Carlo approaches to evaluate probability distributions of interruption duration

Regulatory authorities in many countries, in order to maintain an acceptable balance between appropriate customer service qualities and costs, are introducing a performance-based regulation. These regulations impose penalties-and, in some cases, rewards-that introduce a component of financial risk to an electric power utility due to the uncertainty associated with preserving a specific level of system reliability. In Brazil, for instance, one of the reliability indices receiving special attention by the utilities is the maximum continuous interruption duration (MCID) per customer.This parameter is responsible for the majority of penalties in many electric distribution utilities. This paper describes analytical and Monte Carlo simulation approaches to evaluate probability distributions of interruption duration indices. More emphasis will be given to the development of an analytical method to assess the probability distribution associated with the parameter MCID and the correspond ng penalties. Case studies on a simple distribution network and on a real Brazilian distribution system are presented and discussed.

Power law distribution in education: University entrance examination

We studied the statistical distribution of candidate's performance which is measured through their marks in university entrance examination (Vestibular) of UNESP (Universidade Estadual Paulista) for years 1998, 1999, and 2000. All students are divided in three groups: Physical, Biological and Humanities. We paid special attention to the examination of Portuguese language which is common for all and examinations for the particular area. We observed long ubiquitous power law tails in Physical and Biological sciences. This indicate the presence of strong positive feedback in sciences. We are able to explain completely these statistical distributions through Gradually Truncated Power law distributions which we developed recently to explain statistical behavior of financial market. The statistical distribution in case of Portuguese language and humanities is close to normal distribution. We discuss the possible reason for this peculiar behavior.

Mathematical decomposition technique applied to the probabilistic power flow problem

In this paper a framework based on the decomposition of the first-order optimality conditions is described and applied to solve the Probabilistic Power Flow (PPF) problem in a coordinated but decentralized way in the context of multi-area power systems. The purpose of the decomposition framework is to solve the problem through a process of solving smaller subproblems, associated with each area of the power system, iteratively. This strategy allows the probabilistic analysis of the variables of interest, in a particular area, without explicit knowledge of network data of the other interconnected areas, being only necessary to exchange border information related to the tie-lines between areas. An efficient method for probabilistic analysis, considering uncertainty in n system loads, is applied. The proposal is to use a particular case of the point estimate method, known as Two-Point Estimate Method (TPM), rather than the traditional approach based on Monte Carlo simulation. The main feature of the TPM is that it only requires resolve 2n power flows for to obtain the behavior of any random variable. An iterative coordination algorithm between areas is also presented. This algorithm solves the Multi-Area PPF problem in a decentralized way, ensures the independent operation of each area and integrates the decomposition framework and the TPM appropriately. The IEEE RTS-96 system is used in order to show the operation and effectiveness of the proposed approach and the Monte Carlo simulations are used to validation of the results. © 2011 IEEE.

Probabilistic analysis of the distributed power generation in weakly meshed distribution systems

This paper presents an approach for probabilistic analysis of unbalanced three-phase weakly meshed distribution systems considering uncertainty in load demand. In order to achieve high computational efficiency this approach uses both an efficient method for probabilistic analysis and a radial power flow. The probabilistic approach used is the well-known Two-Point Estimate Method. Meanwhile, the compensation-based radial power flow is used in order to extract benefits from the topological characteristics of the distribution systems. The generation model proposed allows modeling either PQ or PV bus on the connection point between the network and the distributed generator. In addition allows control of the generator operating conditions, such as the field current and the power delivery at terminals. Results on test with IEEE 37 bus system is given to illustrate the operation and effectiveness of the proposed approach. A Monte Carlo Simulations method is used to validate the results. © 2011 IEEE.