920 resultados para probability distribution
Resumo:
By introducing the scattering probability of a subsurface defect (SSD) and statistical distribution functions of SSD radius, refractive index, and position, we derive an extended bidirectional reflectance distribution function (BRDF) from the Jones scattering matrix. This function is applicable to the calculation for comparison with measurement of polarized light-scattering resulting from a SSD. A numerical calculation of the extended BRDF for the case of p-polarized incident light was performed by means of the Monte Carlo method. Our numerical results indicate that the extended BRDF strongly depends on the light incidence angle, the light scattering angle, and the out-of-plane azimuth angle. We observe a 180 degrees symmetry with respect to the azimuth angle. We further investigate the influence of the SSD density, the substrate refractive index, and the statistical distributions of the SSD radius and refractive index on the extended BRDF. For transparent substrates, we also find the dependence of the extended BRDF on the SSD positions. (c) 2006 Optical Society of America.
Resumo:
We modeled the probability of capturing Pacif ic mackerel (Scomber japonicus) larvae as a function of environmental variables for the Southern California Bight (SCB) most years from 1951 through 2008 and Mexican waters offshore of Baja California from 1951 through 1984. The model exhibited acceptable fit, as indicated by the area under a receiver-operating-characteristic curve of 0.80 but was inconsistent with the zero catches that occurred frequently in the 2000s. Two types of spawners overlapped spatially within the survey area: those that exhibited peak spawning during April in the SCB at about 15.5°C and a smaller group that exhibited peak spawning in August near Punta Eugenia, Mexico, at 20°C or greater. The SCB generally had greater zooplankton than Mexican waters but less appropriate (lower) geostrophic f lows. Mexican waters generally exhibited greater predicted habitat quality than the SCB in cold years. Predicted quality of the habitat in the SCB was greater from the 1980s to 2008 than in the earlier years of the survey primarily because temperatures and geostrophic flows were more appropriate for larvae. However, stock size the previous year had a larger effect on predictions than any environmental variable, indicating that larval Pacific mackerel did not fully occupy the suitable habitat during most years.
Resumo:
Lar lake, with the international UTM specification of 39S 579680 3976567 & 39S 589930 3976184 is Situated in Lar national Park with an aerial distance of 55 Km of Tehran along Haraz road. The present research is carried out as part of a comprehensives Plan for assessment of bioresearches of Lar lake & the rivers flowing into it. This research includes examination of there benthic Samplings performed in Lar lake and each of the related rivers including Delichaee, Ab-e-sefid , Alarm & Lar (Kamardasht).Tubifex and Chironomus genus were found to have the highest frequencies of occurrence in the lake with %77.117 & %21.823 respectively followed by Chironomidae and Simulidae from the Diptera order which accounted for %72.328 and %13.812 occurrences in four rivers examined in the Study. The benthic biomass at various examined Sites and the average wet weight of the benthic biomass in station No one in the lake Was 17.397g and the figure for the examined site in Alarm was 20.242 g which were the highest level among Other examination stations the index for the abundance of species in Alarm river was greater than the rest of the examined rivers with 12.57. A sum of 354 Pieces of brown trouts was caught in the course of sampling which were closely investigated in terms of their digestive tract Content. It was identified that Daphniidae and Chironomus constituted the bulk of eaten items from the lake with %17.985 and %63.973 respectively. Meanwhile, Chironomidae and Simuladae were the most frequently eanten benthos by the fish with %81.47 and %7.93 respectively.The index for the relative length of gut was recorded at 0.49± 0.08 which is well indicative of the carnivorous diet of the fish.The index for the feeding intensity amounted to 138 83 showing that the one year old fish were of more feeding intensity.The coefficient of condition (K) was estimated at 1.02 0.142 for all the caught fish. The average wet weight of the benthos was 10.348 g per square meter which if extended to 700ha surface area of the lake, the total macrobenthic production in the lake would amount to 72730Kg of wet weight or 6510 Kg of dry weight. Since the Secondary Production of macrobenthos have always been double that of their biomass, it is reasonable to assume that the Secondary Production of macrobenthos amount to 145640 Kg by their wet weight and Since the energy transfer in the food chain of the lake from benthos to fish is 10 percent, the fish production Capacity Coming from benthic resources of the lake (Lar) would be 14.5 MT, half of which (7000-8000MT) could annually be harvested. Further more, the actual fish Production Capacity might exceed the projected level Since Daphnia, Rotifers and Ostracoda which belong to Zooplanktons, play a part in the natural diet of trout. Meanwhile, rivers Play a major role in fish nutrition and the annual fish production in Delichaee river is about 4481.8Kg while the figures for Ab-e-sefid, Alerm and Lar rivers are 2370.7 4848.7 and 2586.2 Kg respectively, that further increase fish Production in the area and every year half of these resources can be exploitable from the river & the lake.Nevertheless, due to ecological & biological importance of rivers and the probability of environmental Pollution, devastation of natural fish habitats & their nursery grounds, Sport fishing is not recommended at all.
Resumo:
This paper is concerned with the probability density function of the energy of a random dynamical system subjected to harmonic excitation. It is shown that if the natural frequencies and mode shapes of the system conform to the Gaussian Orthogonal Ensemble, then under common types of loading the distribution of the energy of the response is approximately lognormal, providing the modal overlap factor is high (typically greater than two). In contrast, it is shown that the response of a system with Poisson natural frequencies is not approximately lognormal. Numerical simulations are conducted on a plate system to validate the theoretical findings and good agreement is obtained. Simulations are also conducted on a system made from two plates connected with rotational springs to demonstrate that the theoretical findings can be extended to a built-up system. The work provides a theoretical justification of the commonly used empirical practice of assuming that the energy response of a random system is lognormal.
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A location- and scale-invariant predictor is constructed which exhibits good probability matching for extreme predictions outside the span of data drawn from a variety of (stationary) general distributions. It is constructed via the three-parameter {\mu, \sigma, \xi} Generalized Pareto Distribution (GPD). The predictor is designed to provide matching probability exactly for the GPD in both the extreme heavy-tailed limit and the extreme bounded-tail limit, whilst giving a good approximation to probability matching at all intermediate values of the tail parameter \xi. The predictor is valid even for small sample sizes N, even as small as N = 3. The main purpose of this paper is to present the somewhat lengthy derivations which draw heavily on the theory of hypergeometric functions, particularly the Lauricella functions. Whilst the construction is inspired by the Bayesian approach to the prediction problem, it considers the case of vague prior information about both parameters and model, and all derivations are undertaken using sampling theory.
Resumo:
Presented in this paper is a mathematical model to calculate the probability of the sediment incipient motion, in which the effects of the fluctuating pressure and the seepage are considered. The instantaneous bed shear velocity and the pressure gradient on the bed downstream of the backward-facing step flow are obtained according to the PIV measurements. It is found that the instantaneous pressure gradient on the bed obeys normal distribution. The probability of the sediment incipient motion on the bed downstream of the backward-facing step flow is given by the mathematical model. The predicted results agree well with the experiment in the region downstream of the reattachment point while a large discrepancy between the theory and experiment is seen in the region near the reattachment point. The possible reasons for this discrepancy are discussed.
Resumo:
The sequence distribution of the monomeric units in the styrene-acrylic acid copolymer has been obtained by calculation. The probability of long sequences of styrene increases with an increase in the content of the monomer in the copolymer. The highest distribution of short sequences of styrene takes place for the copolymer containing equimolecular amounts of styrene and acrylic acid. The copolymer which has this latter structure is inadequate for the synthesis of highly active supported complexes. When the distributions of long and short sequences of styrene are approximately equal, the activity of the Nd and Fe prepared polymer complexes is higher.
Resumo:
Based on the ray theory and Longuet-Higgins's linear,model of sea waves, the joint distribution of wave envelope and apparent wave number vector is established. From the joint distribution, we define a new concept, namely the outer wave number spectrum, to describe the outer characteristics of ocean waves. The analytical form of the outer wave number spectrum, the probability distributions of the apparent wave number vector and its components are then derived. The outer wave number spectrum is compared with the inner wave number spectrum for the average status of wind-wave development corresponding to a peakness factor P = 3. Discussions on the similarity and difference between the outer wave number spectrum and inner one are also presented in the paper. (C) 2002 Elsevier Science Ltd. All rights reserved.
Resumo:
The class of all Exponential-Polynomial-Trigonometric (EPT) functions is classical and equal to the Euler-d’Alembert class of solutions of linear differential equations with constant coefficients. The class of non-negative EPT functions defined on [0;1) was discussed in Hanzon and Holland (2010) of which EPT probability density functions are an important subclass. EPT functions can be represented as ceAxb, where A is a square matrix, b a column vector and c a row vector where the triple (A; b; c) is the minimal realization of the EPT function. The minimal triple is only unique up to a basis transformation. Here the class of 2-EPT probability density functions on R is defined and shown to be closed under a variety of operations. The class is also generalised to include mixtures with the pointmass at zero. This class coincides with the class of probability density functions with rational characteristic functions. It is illustrated that the Variance Gamma density is a 2-EPT density under a parameter restriction. A discrete 2-EPT process is a process which has stochastically independent 2-EPT random variables as increments. It is shown that the distribution of the minimum and maximum of such a process is an EPT density mixed with a pointmass at zero. The Laplace Transform of these distributions correspond to the discrete time Wiener-Hopf factors of the discrete time 2-EPT process. A distribution of daily log-returns, observed over the period 1931-2011 from a prominent US index, is approximated with a 2-EPT density function. Without the non-negativity condition, it is illustrated how this problem is transformed into a discrete time rational approximation problem. The rational approximation software RARL2 is used to carry out this approximation. The non-negativity constraint is then imposed via a convex optimisation procedure after the unconstrained approximation. Sufficient and necessary conditions are derived to characterise infinitely divisible EPT and 2-EPT functions. Infinitely divisible 2-EPT density functions generate 2-EPT Lévy processes. An assets log returns can be modelled as a 2-EPT Lévy process. Closed form pricing formulae are then derived for European Options with specific times to maturity. Formulae for discretely monitored Lookback Options and 2-Period Bermudan Options are also provided. Certain Greeks, including Delta and Gamma, of these options are also computed analytically. MATLAB scripts are provided for calculations involving 2-EPT functions. Numerical option pricing examples illustrate the effectiveness of the 2-EPT approach to financial modelling.
Resumo:
The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.
Resumo:
The chain growth probability (alpha value) is one of the most significant parameters in Fischer-Tropsch (FT) synthesis. To gain insight into the chain growth probability, we systematically studied the hydrogenation and C-C coupling reactions with different chain lengths on the stepped Co(0001) surface using density functional theory calculations. Our findings elucidate the relationship between the barriers of these elementary reactions and the chain length. Moreover, we derived a general expression of the chain growth probability and investigated the behavior of the alpha value observed experimentally. The high methane yield results from the lower chain growth rate for C-1 + C-1 coupling compared with the other coupling reactions. After C-1, the deviation of product distribution in FT synthesis from the Anderson-Schulz-Flory distribution is due to the chain length-dependent paraffin/olefin ratio. (C) 2008 Elsevier Inc. All rights reserved.
Resumo:
In the past few decades, Coxian phase-type distributions have become increasingly more popular as a means of representing survival times. In healthcare, they are considered suitable for modelling the length of stay of patients in hospital and more recently for modelling the patient waiting times in Accident and Emergency Departments. The Coxian phase-type distribution has not only been shown to provide a good representation of real survival data, but its interpretation seems reasonably initiative to the medical experts. The drawback, however, is fitting the distribution to the data. There have been many attempts at accurately estimating the Coxian phase-type parameters. This paper wishes to examine the most promising of the approaches reported in the literature to determine the most accurate. Three performance measures are introduced to assess the fitting process of the algorithms along with the likelihood values and AIC to examine the goodness of fit and complexity of the model. Previous research suggests that the fitting process is strongly influenced by the initial parameter estimates and the data itself being quite variable. To overcome this, one experiment in this research paper will use the same initial parameter values for each estimation and perform the fits on the data simulated from a Coxian phase-type distribution with known parameters.
Resumo:
In this letter, we investigate the distribution of the phase component of the complex received signal observed in practical experiments using body area networks. Two phase distributions, the recently proposed kappa-mu and eta-mu probability densities, which together encompass the most widely used fading models, namely Semi-Gaussian, Rayleigh, Hoyt, Rice, and Nakagami-m, have been compared with measurement data. The kappa-mu distribution has been found to provide the best fit over a range of on-body links, while the user was mobile. The experiments were carried out in two dissimilar indoor environments at opposite ends of the multipath spectrum. It has also been found that the uniform phase distribution has not arisen in anyone of the experiments.
Resumo:
This paper studies the Demmel condition number of Wishart matrices, a quantity which has numerous applications to wireless communications, such as adaptive switching between beamforming and diversity coding, link adaptation, and spectrum sensing. For complex Wishart matrices, we give an exact analytical expression for the probability density function (p.d.f.) of the Demmel condition number, and also derive simplified expressions for the high tail regime. These results indicate that the condition of complex Wishart matrices is dominantly decided by the difference between the matrix dimension and degree of freedom (DoF), i.e., the probability of drawing a highly ill conditioned matrix decreases considerably when the difference between the matrix dimension and DoF increases. We further investigate real Wishart matrices, and derive new expressions for the p.d.f. of the smallest eigenvalue, when the difference between the matrix dimension and DoF is odd. Based on these results, we succeed to obtain an exact p.d.f. expression for the Demmel condition number, and simplified expressions for the high tail regime.
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Electron energy probability functions measured with a passively compensated Langmuir probe in asymmetric capacitively coupled hydrogen and deuterium plasmas exhibit structure. The otherwise relatively continuous distribution appears to have an abrupt peak in electron density near 5 eV. This structure occurs at a higher energy in deuterium than hydrogen and there is a correlation between floating potential and the voltage at which the structure is observed in the second derivative of the I(V) characteristic. While the cause of the structure has yet to be clarified, spectroscopic observations and computer-based hydrogen models indicate that the high energy tail of the distribution is strongly modulated during the radio frequency cycle. The effect of this modulation on plasma properties and probe measurements has yet to be explored. (C) 1999 American Institute of Physics. [S0003-6951(99)00819-0].