Uma nova família de distribuições denominada distribuição beta generalizada semi-normal, que inclui algumas distribuições importantes como casos especiais, tais como as distribuições semi-normal e generalizada semi-normal (Cooray e Ananda, 2008), é proposta neste trabalho. Para essa nova família de distribuições, foi realizado o estudo da função densidade probabilidade, função de distribuição acumulada e da função de taxa de falha (ou risco), que não dependeram de funções matemáticas complicadas. Obteve-se uma expressão formal para os momentos, função geradora de momentos, função densidade da distribuição de estatística de ordem, desvios médios, entropia, contabilidade e para as curvas de Bonferroni e Lorenz. Examinaram-se os estimadores de máxima verossimilhança dos parâmetros e deduziu- se a matriz de informação esperada. Neste trabalho é proposto, também, um modelo de regressão utilizando a distribuição beta generalizada semi-normal. A utilidade dessa nova distribuição é ilustrada através de dois conjuntos de dados, mostrando que ela é mais flexível na análise de dados de tempo de vida do que outras distribuições existentes na literatura.; A new family of distributions so-called beta generalized half-normal distribution...

No estudo dos raios cósmicos de ultra alta energia utilizando detectores de superfície a energia da partícula primária é estimada pela distribuição lateral (LDF - Lateral Distribution Function), que descreve a amplitude do sinal das estações em função da distância ao centro do chuveiro. Entretanto, com exceção da estimativa do centro do chuveiro, não se utiliza a LDF para obter mais nenhuma informação sobre o chuveiro, talvez porque ela não possua uma parametrização que a descreva completamente, especialmente para os chuveiros com energias mais altas. As primeiras interações dos raios cósmicos com a atmosfera são determinantes para o desenvolvimento dos chuveiros atmosféricos extensos. Tais interações dependem, entre outras coisas, da composição química dos raios cósmicos. Diferenças nessas interações podem causar alterações nas flutuações da distribuição lateral. Através de simulações dos chuveiros com diferentes partículas primárias pode ser possível estimar a composição dos raios cósmicos de ultra alta energia, comparando as flutuações das distribuições laterais de eventos reais com as de eventos simulados. Uma das grandezas relevantes para a flutuação da LDF é a incerteza do sinal das estações. O framework de análise do Observatório Pierre Auger aplica uma correção parametrizada empiricamente à incerteza do sinal das estações. Neste trabalho foi apresentada uma justificativa estatística para esta correção...

Neste trabalho, o método de Monte Carlo é aplicado à função distribuição de energia de corpo negro nas linhas de absorção (função distribuição ALB) para considerar o efeito espectral no cálculo da transferência de calor por radiação em meios participantes. A metodologia combina o robusto e flexível método de Monte Carlo com a função distribuição ALB, que incorpora simultaneamente o efeito de um grande número de linhas espectrais. A implementação proposta estabelece uma relação simples e direta entre a função distribuição ALB e a função distribuição cumulativa do método de Monte Carlo, o que facilita a implementação da técnica e proporciona eficiência computacional. A verificação da metodologia foi realizada através da comparação de seus resultados com uma série de soluções apresentadas na literatura utilizando-se tanto o modelo da somaponderada- de-gases-cinzas baseado nas linhas espectrais quanto a integração linha-por-linha, considerando meios participantes não-homogêneos e não-isotérmicos constituídos de vapor d’água, dióxido de carbono e espécies não-participantes. O método de Monte Carlo aplicado à função distribuição ALB foi utilizado na obtenção de vários resultados para avaliar as aproximações relativas ao modelo da somaponderada- de-gases-cinzas...

Given the busy period major importance in queuing systems, it is also relevant to study the busy cycle. In this work some interesting results on M|G|∞ queue system busy cycle distribution are presented. They are emphasized for the M|D|∞ queue system and a numerical method to compute the M|D|∞ queue system busy cycle distribution function is presented.

In decision-making problems under uncertainty, mean-variance analysis consistent with expected utility theory plays an important role in analysing preferences for different alternatives. In this paper, a new approach for mean-variance analysis based on cumulative distribution functions is proposed. Using simulation, a new algorithm is developed, which generates pairs of random variables to be representative for each pair of uncertain alternatives. The proposed model is concerned with financial investment for risk-averse investors with non-negative lotteries. Furthermore, the proposed technique in this paper can be applies to different distribution functions for lotteries or utility functions.; Khwazbeen S. Fatah, Peng Shi, Jamal R.M. Ameen, Ronald J. Wiltshire

In this work we introduce an analytical model for square Gate All Around (GAA) MOSFETs with rounded corners including quantum effects. With the model developed it is possible to provide an analytical description of the 2D inversion charge distribution function (ICDF) in devices of different sizes and for all the op erational regimes. The accuracy of the model is verified by comparing with data obtai ned by means of a 2D numerical simulator that self-consistently solves the Poi sson and Schr ??odinger equations. The expressions presented here are useful to achieve a good d escription of the physics of these transistors; in particular, of the quantization effect s on the inversion charge. The analytical ICDF obtained is used to calculate important par ameters from the device compact modeling viewpoint, such as the inversion charge ce ntroid and the gate-to- channel capacitance, which are modeled for different device g eometries and biases.

Within the Dyson–Schwinger equation formulation of QCD, a rainbow ladder truncation is used to calculate the pion valence-quark distribution function (PDF). The gap equation is renormalized at a typical hadronic scale, of order 0.5 GeV, which is also set as the default initial scale for the pion PDF. We implement a corrected leading-order expression for the PDF which ensures that the valence-quarks carry all of the pion's light-front momentum at the initial scale. The scaling behavior of the pion PDF at a typical partonic scale of order 5.2 GeV is found to be (1−x)ν, with ν≃1.6, as x approaches one.; Lei Chang, Anthony W. Thomas

Luby Transform (LT) code over finite field is a recent research topic. In order to find out the properties of LT codes over finite field, a novel degree distribution function is proposed in this paper. The main thinking of our developed distribution function is to improve the decoding success rate with the same overhead, and still to keep the sparse property for the encoding matrix. Numerical simulations are used to show the general performance of our novel function. Various simulation results show that in the environment of LT codes over finite field, our new degree distribution function performs much better than the degree distribution functions proposed by Luby as the field size increasing. In conclusion, our novel degree distribution function is more suitable to be used in LT codes over finite field.

The Airy distribution function describes the probability distribution of the area under a Brownian excursion over a unit interval. Surprisingly, this function has appeared in a number of seemingly unrelated problems, mostly in computer science and graph theory. In this paper, we show that this distribution also appears in a rather well studied physical system, namely the fluctuating interfaces. We present an exact solution for the distribution P(h_m,L) of the maximal height h_m (measured with respect to the average spatial height) in the steady state of a fluctuating interface in a one dimensional system of size L with both periodic and free boundary conditions. For the periodic case, we show that P(h_m,L)=L^{-1/2}f(h_m L^{-1/2}) for all L where the function f(x) is the Airy distribution function. This result is valid for both the Edwards-Wilkinson and the Kardar-Parisi-Zhang interfaces. For the free boundary case, the same scaling holds P(h_m,L)=L^{-1/2}F(h_m L^{-1/2}), but the scaling function F(x) is different from that of the periodic case. We compute this scaling function explicitly for the Edwards-Wilkinson interface and call it the F-Airy distribution function. Numerical simulations are in excellent agreement with our analytical results. Our results provide a rather rare exactly solvable case for the distribution of extremum of a set of strongly correlated random variables. Some of these results were announced in a recent Letter [ S.N. Majumdar and A. Comtet...

This work proposes a parametric equilibrium distribution function F_eq to be applied to the gyrokinetic studies of the Finite Orbit Width behavior of guiding centers representing several species encountered in axisymmetric tokamak plasma, as fusion products, thermal bulk and energetic particles from Ion Cyclotron Radiation Heating and Negative Neutral Beam Injections. After the analysis of the basic results of orbit theory obtained with a particularly convenient orbit coordinates set, it is shown how the proposed F_eq satisfies the two conditions that make it an equilibrium distribution function: (i) it must depend only on the constants of motion and adiabatic invariants, and (ii) the guiding centers must remain confined for suitably long time. Furthermore, the F_eq can be modeled, with a proper choice of its parameters, to reproduce the most common distribution functions. A local Maxwellian distribution function is obtained for the thermal plasma in the Zero Orbit Width approximation. For the fusion \alpha particles, F_eq can also reproduce the Slowing Down (SD) distribution function. More generally, for supra-thermal particles, when external heatings are present, such as (N)NBI and ICRH, the proposed model distribution function shows similarities with the anisotropic SD and the biMaxwellian distribution functions. F_eq can be used to fit experimental profiles and it could provide a useful tool for experimental and numerical data analysis. Moreover...

We compare three methods to measure the count-in-cell probability density function of galaxies in a spectroscopic redshift survey. From this comparison we found that when the sampling is low (the average number of object per cell is around unity) it is necessary to use a parametric method to model the galaxy distribution. We used a set of mock catalogues of VIPERS, in order to verify if we were able to reconstruct the cell-count probability distribution once the observational strategy is applied. We find that in the simulated catalogues, the probability distribution of galaxies is better represented by a Gamma expansion than a Skewed Log-Normal. Finally, we correct the cell-count probability distribution function from the angular selection effect of the VIMOS instrument and study the redshift and absolute magnitude dependency of the underlying galaxy density function in VIPERS from redshift $0.5$ to $1.1$. We found very weak evolution of the probability density distribution function and that it is well approximated, independently from the chosen tracers, by a Gamma distribution.; Comment: 14 pages, 11 figures, 2 tables

In this article it is shown that in an equilibrium classical canonical ensemble of molecules with two-body interaction and external field full Gibbs distribution can be uniquely expressed in terms of a reduced two-particle distribution function. This means that while a number of particles $N$ and a volume $V$ are fixed the reduced two-particle distribution function contains as much information about the equilibrium system as the whole canonical distribution. The latter is represented as an absolutely convergent power series relative to the reduced two-particle distribution function. As an example a linear term of this expansion is calculated. It is also shown that Gibbs distribution function can de expressed in terms of reduced distribution function of the first order and pair correlation function.That is the later two functions contain the whole information about system under consideration.; Comment: This work was reported on International conference "Mathematical physics and its applications" in Samara, Russia, 7-13 september 2008

Wigner distribution function has much importance in quantum statistical mechanics. It finds applications in various disciplines of physics including condense matter, quantum optics, to name but a few. Wigner distribution function is introduced by E. Wigner in 1932. However, there is no analytical derivation of Wigner distribution function in the literatures, to date. In this paper, a simple analytical derivation of Wigner distribution function is presented. Our derivation is based on two assumptions, these are A) by taking the integral of Wigner distribution function, with respect to configuration space, the momentum space distribution function is obtained B) WDF is real. Similarly, and in addition to Wigner distribution function, the distribution function of Sobouti-Nasiri, which is imaginary, is also derived.

In the beginning of the 1950's, Wigner introduced a fundamental deformation from the canonical quantum mechanical harmonic oscillator, which is nowadays sometimes called a Wigner quantum oscillator or a parabose oscillator. Also, in quantum mechanics the so-called Wigner distribution is considered to be the closest quantum analogue of the classical probability distribution over the phase space. In this article, we consider which definition for such distribution function could be used in the case of non-canonical quantum mechanics. We then explicitly compute two different expressions for this distribution function for the case of the parabose oscillator. Both expressions turn out to be multiple sums involving (generalized) Laguerre polynomials. Plots then show that the Wigner distribution function for the ground state of the parabose oscillator is similar in behaviour to the Wigner distribution function of the first excited state of the canonical quantum oscillator.; Comment: 20 pages, 2 EPS figures, published in Journal of Physics A

The availability of neutron spallation-source instruments that provide total scattering powder diffraction has led to an increased application of real-space structure analysis using the pair distribution function. Currently, the analytical treatment of finite size effects within pair distribution refinement procedures is limited. To that end, an envelope function is derived which transforms the pair distribution function of an infinite solid into that of a spherical particle with the same crystal structure. Distributions of particle sizes are then considered, and the associated envelope function is used to predict the particle size distribution of an experimental sample of gold nanoparticles from its pair distribution function alone. Finally, complementing the wealth of existing diffraction analysis, the peak broadening for the structure factor of spherical particles, expressed as a convolution derived from the envelope functions, is calculated exactly for all particle size distributions considered, and peak maxima, offsets, and asymmetries are discussed.; Comment: 7 pages, 6 figures

From a coupling model between the Boltzmann transport equation and the quantum Liouville equation, we have developed a simulator based on the Wigner distribution function (WDF) approach that can be applied to resonant tunneling diodes (RTDs) and other vertical transport quantum devices. In comparison to previous WDF simulators, the tool allows one to extend the simulation domains up to hundreds of nanometers, which are the typical dimensions required for the study of actual multilayer structures. With these improvements, a level of agreement between theory and experiment comparable to that obtained by using other simulators based on Green functions has been achieved. The results of this work reveal that the WDF formalism can be alternatively used to study the behavior of actual multilayered RTDs.

We want to know how is the harmonic distribution and in order to do so we will implement this distribution into Wikipedia where we will describe its probability density function, its cumulative distribution function (here we can calculate the quantiles), the moments (we can calculate the skewness and kurtosis) and the distribution estimators among other parametres. With the parameters that we estimate we will see an example as to calculate these parameters. Finally we discuss how we can connect our Harmonic Distribution with other distributions that are similar.; Volem saber com és la Distribució Harmònica, aleshores el que farem amb aquest treball és implementar aquesta distribució a Wikipedia on descriurem la seva funció de densitat de probabilitat, la funció de distribució (d'aquí podrem extreure els quantils d'aquesta distribució), els moments (on farem un petit èmfasi en l'asimetria i la curtosi) o els estimadors de la distribució entre d'altres. Amb els paràmetres que estimarem, veurem en un exemple com poder-ho calcular. Finalment esmentarem com podem relacionar la nostra distribució Harmònica amb altres distribucions semblants.

This paper shows that a processor hybrid of analog electronics and optics can quickly calculate 1-dimension lines with the function of Wigner distribution by using bi-dimensional input signals.

Silicene is the counterpart of graphene and its potential applications as a part of the current electronics, based in silicon, make it a very important system to study. We perform molecular dynamics simulations and analyze the structure of a two dimensional array of Si atoms by means of the radial distribution function at different temperatures and densities. As a first approach, the Lennard-Jones potential is used and two sets of parameters are tested. We find that the radial distribution function does not change with the parameters and resembles the corresponding to the (111) surface of the FCC structure. The liquid phase appears at very high temperatures, suggesting a very stable system in the solid phase.

This work presents a study of the electron suprathermal tails profile and its temperature inside of the magnetic clouds. We have modeled the electron velocity distribution function as a superposition of two populations: core (Maxwellian) and halo (Tsallis or kappa-like). The kappa parameter value, which characterizes the supra-thermal tail of the electron halo component has been estimated. We have found, based upon the events studied here, that there are no significant differences in the values of the kappa parameter, inside and outside magnetic clouds.