Likelihood-based inference for power distributions

This paper considers likelihood-based inference for the family of power distributions. Widely applicable results are presented which can be used to conduct inference for all three parameters of the general location-scale extension of the family. More specific results are given for the special case of the power normal model. The analysis of a large data set, formed from density measurements for a certain type of pollen, illustrates the application of the family and the results for likelihood-based inference. Throughout, comparisons are made with analogous results for the direct parametrisation of the skew-normal distribution.

Determination of relative power distributions in CANEL critical assemblies using catcher foil techniques /

"Contract AT(30-1)-2789."

The effects of transients on photospheric and chromospheric power distributions

We have observed a quiet Sun region with the Swedish 1-meter Solar Telescope (SST) equipped with CRISP Imaging SpectroPolarimeter. High-resolution, high-cadence, H-alpha line scanning images were taken to observe different layers of the solar atmosphere from the photosphere to upper chromosphere. We study the distribution of power in different period-bands at different heights. Power maps of the upper photosphere and the lower chromosphere show suppressed power surrounding the magnetic-network elements, known as "magnetic shadows". These also show enhanced power close to the photosphere, traditionally referred to as"power halos". The interaction between acoustic waves and inclined magnetic fields is generally believed to be responsible for these two effects. In this study we explore if small-scale transients can influence the distribution of power at different heights. We show that the presence of transients, like mottles, Rapid Blueshifted Excursions (RBEs) and Rapid Redshifted Excursions (RREs), can strongly influence the power-maps. The short and finite lifetime of these events strongly affects all powermaps, potentially influencing the observed power distribution. We show that Doppler-shifted transients like RBEs and RREs that occur ubiquitously, can have a dominant effect on the formation ofthe power halos in the quiet Sun. For magnetic shadows, transients like mottles do not seem to have a significant effect in the power suppression around 3 minutes and wave interaction may play a key role here. Our high cadence observations reveal that flows, waves and shocks manifest in presence of magnetic fields to form a non-linear magnetohydrodynamic system.

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.

Location of single line-to-ground faults on distribution feeders using voltage measurements

This paper proposes a dedicated algorithm for lation of single line-to-ground faults in distribution systems. The proposed algorithm uses voltage and current phasors measured at the substation level, voltage magnitudes measured at some buses of the feeder, a database containing electrical, operational and topological parameters of the distribution networks, and fault simulation. Voltage measurements can be obtained using power quality devices already installed on the feeders or using voltage measurement devices dedicated for fault location. Using the proposed algorithm, likely faulted points that are located on feeder laterals geographically far from the actual faulted point are excluded from the results. Assessment of the algorithm efficiency was carried out using a 238 buses real-life distribution feeder. The results show that the proposed algorithm is robust for performing fast and efficient fault location for sustained single line-to-ground faults requiring less than 5% of the feeder buses to be covered by voltage measurement devices. © 2006 IEEE.

Random distributed feedback Raman fiber laser with polarized pumping

In this letter, the polarization properties of a random fiber laser operating via Raman gain and random distributed feedback owing to Rayleigh scattering are investigated for the first time. Using polarized pump, the partially polarized generation is obtained with a generation spectrum exhibiting discrete narrow spectral features contrary to the smooth spectrum observed for the depolarized pump. The threshold, output power, degree of polarization and the state of polarization (SOP) of the lasing can be significantly influenced by the SOP of the pump. Fine narrow spectral components are also sensitive to the SOP of the pump wave. Furthermore, we found that random lasing's longitudinal power distributions are different in the case of polarized and depolarized pumping that results in considerable reduction of the generation slope efficiency for the polarized radiation. Our results indicate that polarization effects play an important role on the performance of the random fiber laser. This work improves the understanding of the physics of random lasing in fibers and makes a step forward towards the establishment of the vector model of random fiber lasers.

Raman fibre laser based amplification in coherent transmission systems

The thesis presents a detailed study of different Raman fibre laser (RFL) based amplification techniques and their applications in long-haul/unrepeatered coherent transmission systems. RFL based amplifications techniques were characterised from different aspects, including signal/noise power distributions, relative intensity noise (RIN), mode structures of induced Raman fibre lasers, and so on. It was found for the first time that RFL based amplification techniques could be divided into three categories in terms of the fibre laser regime, which were Fabry-Perot fibre laser with two FBGs, weak Fabry-Perot fibre laser with one FBG and very low reflection near the input, and random distributed feedback (DFB) fibre laser with one FBG. It was also found that lowering the reflection near the input could mitigate the RIN of the signal significantly, thanks to the reduced efficiency of the Stokes shift from the FW-propagated pump. In order to evaluate the transmission performance, different RFL based amplifiers were evaluated and optimised in long-haul coherent transmission systems. The results showed that Fabry-Perot fibre laser based amplifier with two FBGs gave >4.15 dB Q factor penalty using symmetrical bidirectional pumping, as the RIN of the signal was increased significantly. However, random distributed feedback fibre laser based amplifier with one FBG could mitigate the RIN of the signal, which enabled the use of bidirectional second order pumping and consequently give the best transmission performance up to 7915 km. Furthermore, using random DFB fibre laser based amplifier was proved to be effective to combat the nonlinear impairment, and the maximum reach was enhanced by >28% in mid-link single/dual band optical phase conjugator (OPC) transmission systems. In addition, unrepeatered transmission over >350 km fibre length using RFL based amplification technique were presented experimentally using DP-QPSK and DP-16QAM transmitter.

A Review on the Characterization of Signals and Systems by Power Law Distributions

Power laws, also known as Pareto-like laws or Zipf-like laws, are commonly used to explain a variety of real world distinct phenomena, often described merely by the produced signals. In this paper, we study twelve cases, namely worldwide technological accidents, the annual revenue of America׳s largest private companies, the number of inhabitants in America׳s largest cities, the magnitude of earthquakes with minimum moment magnitude equal to 4, the total burned area in forest fires occurred in Portugal, the net worth of the richer people in America, the frequency of occurrence of words in the novel Ulysses, by James Joyce, the total number of deaths in worldwide terrorist attacks, the number of linking root domains of the top internet domains, the number of linking root domains of the top internet pages, the total number of human victims of tornadoes occurred in the U.S., and the number of inhabitants in the 60 most populated countries. The results demonstrate the emergence of statistical characteristics, very close to a power law behavior. Furthermore, the parametric characterization reveals complex relationships present at higher level of description.

Optimum power allocation for parallel Gaussian channels with arbitrary input distributions

The mutual information of independent parallel Gaussian-noise channels is maximized, under an average power constraint, by independent Gaussian inputs whose power is allocated according to the waterfilling policy. In practice, discrete signalling constellations with limited peak-to-average ratios (m-PSK, m-QAM, etc) are used in lieu of the ideal Gaussian signals. This paper gives the power allocation policy that maximizes the mutual information over parallel channels with arbitrary input distributions. Such policy admits a graphical interpretation, referred to as mercury/waterfilling, which generalizes the waterfilling solution and allows retaining some of its intuition. The relationship between mutual information of Gaussian channels and nonlinear minimum mean-square error proves key to solving the power allocation problem.

Asymptotic normality in mixtures of power series distributions

The problem of estimating the individual probabilities of a discrete distribution is considered. The true distribution of the independent observations is a mixture of a family of power series distributions. First, we ensure identifiability of the mixing distribution assuming mild conditions. Next, the mixing distribution is estimated by non-parametric maximum likelihood and an estimator for individual probabilities is obtained from the corresponding marginal mixture density. We establish asymptotic normality for the estimator of individual probabilities by showing that, under certain conditions, the difference between this estimator and the empirical proportions is asymptotically negligible. Our framework includes Poisson, negative binomial and logarithmic series as well as binomial mixture models. Simulations highlight the benefit in achieving normality when using the proposed marginal mixture density approach instead of the empirical one, especially for small sample sizes and/or when interest is in the tail areas. A real data example is given to illustrate the use of the methodology.

Testing projected wild bee distributions in agricultural habitats: predictive power depends on species traits and habitat type

Species distribution models (SDM) are increasingly used to understand the factors that regulate variation in biodiversity patterns and to help plan conservation strategies. However, these models are rarely validated with independently collected data and it is unclear whether SDM performance is maintained across distinct habitats and for species with different functional traits. Highly mobile species, such as bees, can be particularly challenging to model. Here, we use independent sets of occurrence data collected systematically in several agricultural habitats to test how the predictive performance of SDMs for wild bee species depends on species traits, habitat type, and sampling technique. We used a species distribution modeling approach parametrized for the Netherlands, with presence records from 1990 to 2010 for 193 Dutch wild bees. For each species, we built a Maxent model based on 13 climate and landscape variables. We tested the predictive performance of the SDMs with independent datasets collected from orchards and arable fields across the Netherlands from 2010 to 2013, using transect surveys or pan traps. Model predictive performance depended on species traits and habitat type. Occurrence of bee species specialized in habitat and diet was better predicted than generalist bees. Predictions of habitat suitability were also more precise for habitats that are temporally more stable (orchards) than for habitats that suffer regular alterations (arable), particularly for small, solitary bees. As a conservation tool, SDMs are best suited to modeling rarer, specialist species than more generalist and will work best in long-term stable habitats. The variability of complex, short-term habitats is difficult to capture in such models and historical land use generally has low thematic resolution. To improve SDMs’ usefulness, models require explanatory variables and collection data that include detailed landscape characteristics, for example, variability of crops and flower availability. Additionally, testing SDMs with field surveys should involve multiple collection techniques.

A compound class of Weibull and power series distributions

In this paper we introduce the Weibull power series (WPS) class of distributions which is obtained by compounding Weibull and power series distributions where the compounding procedure follows same way that was previously carried out by Adamidis and Loukas (1998) This new class of distributions has as a particular case the two-parameter exponential power series (EPS) class of distributions (Chahkandi and Gawk 2009) which contains several lifetime models such as exponential geometric (Adamidis and Loukas 1998) exponential Poisson (Kus 2007) and exponential logarithmic (Tahmasbi and Rezaei 2008) distributions The hazard function of our class can be increasing decreasing and upside down bathtub shaped among others while the hazard function of an EPS distribution is only decreasing We obtain several properties of the WPS distributions such as moments order statistics estimation by maximum likelihood and inference for a large sample Furthermore the EM algorithm is also used to determine the maximum likelihood estimates of the parameters and we discuss maximum entropy characterizations under suitable constraints Special distributions are studied in some detail Applications to two real data sets are given to show the flexibility and potentiality of the new class of distributions (C) 2010 Elsevier B V All rights reserved

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.

The gradually truncated Levy flight for systems with power-law distributions

Power-law distributions have been observed in various economical and physical systems. Levy flights have infinite variance which discourage a physical approach. We introduce a class of stochastic processes, the gradually truncated Levy flight in which large steps of a Levy flight are gradually eliminated. It has finite variance and the system can be analyzed in a closed form. We applied the present method to explain the distribution of a particular economical index. The present method can be applied to describe time series in a variety of fields, i.e. turbulent flow, anomalous diffusion, polymers, etc. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Power laws, Discontinuities and Regional City Size Distributions

Urban systems are manifestations of human adaptation to the natural environment. City size distributions are the expression of hierarchical processes acting upon urban systems. In this paper, we test the entire city size distributions for the southeastern and southwestern United States (1990), as well as the size classes in these regions for power law behavior. We interpret the differences in the size of the regional city size distributions as the manifestation of variable growth dynamics dependent upon city size. Size classics in the city size distributions are snapshots of stable states within urban systems in flux.