共查询到19条相似文献，搜索用时 218 毫秒
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对一实验数据组进行线性多重回归,如果数据的涨落服从泊松概率分布,常用方法不能给出准确的解。一般地,是假设各泊松分布的形状近似于高斯分布,给出近似解。因此,也存在着人所共知的拟合曲线下的面积亏损问题。本文从最大或然法出发,不加任何假设,严格推导了求解泊松分布线性多重回归的一种方法。按这一方法,“面积亏损”问题在计算精度范围内也得到彻底解决。 相似文献
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本文提供了日珥发射线光谱分析的一种新方法。它允许源函数随光学深度变化,采用非线性最小二乘拟合,直接从观测轮廓同时确定线心光学厚度τ_0、Doppler宽度△λ_D和源函数变化因子α。 本文用这个方法给出了对文献[1]十个日珥早 Balmer 线的分析结果。这些结果表明,自反变H_α线源函数向日珥内增加,中心源函数是边缘的1.2～2.5倍;忽略源函数的这种变化,将使H_α线τ_0的确定明显偏大;日珥的自吸收减弱亦与源函数变化有关。 对日珥源函数变化的讨论,支持关于日珥辐射激发的主要机制是散射太阳入射辐射的论点。 相似文献
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本文对云南天文台1981年5月16日3B级双带大耀斑环(0922UT)的H_α—SSHG光谱资料作了初步的数据处理。采用非线性函数的最小二乘曲线拟合方法,从光谱轮廓求得圆面耀斑环的线心光学厚度τ_0、Doppler宽度Δλ_D平均能源函数S_λ及视向速度V_(11)的二维分布,为处理具有时空序列的光谱资料提供了一种数值方法。计算结果表明,耀斑环系内的物质由环顶沿两环腿向色球层溅落;用色球蒸发模型解释环中的物质来源较为合理。 相似文献
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《天文学进展》2014,(3)
云核质量函数(CMF)是分子云中致密云核的一个基本观测性质,被用来研究恒星的初始质量函数(IMF)的成因。CMF可以用积分和微分两种形式来表达。样本较小时,积分形式的CMF拟合出的结果能够清晰地反映出云核的数目;样本较大时,微分形式的CMF可以合并数据明确地表述CMF。一般来说,CMF有幂律和正态对数两种函数形式。在湍流存在的情况下,正态对数函数可以更好地拟合CMF;幂律形式的CMF谱指数在一定范围内波动,其大小与天区和样本有关。Salpeter提出恒星的初始质量函数(IMF)是一个幂律函数,很多研究认为CMF与IMF是相似的。而近期的一些研究工作认为CMF与IMF是不相同的,这主要有三方面的原因:(1)用一个具体的幂律函数去拟合一个任意的积分函数是不可靠的;(2)只有当M Mmax(或者Mmax-→∞)时,积分形式的CMF可以近似地认为是幂律形式的;(3)采用Monte Carlo方法拟合CMF能够增加拟合结果的可信度。 相似文献
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人卫光学观测中大异常值的剔除方法 总被引：2，自引：0，他引：2
本文详细讨论了人造卫星学观测中大异常值的剔除问题，我们首先将复杂的非线性问题，利用初始轨道，将它转化为便于数学处理的线性模型，用时间差△Ｔ，以及轨道面法向差△θ两个量来分析判别，并提出了一种采用截断最小二乘的Ｌ－估计目标函数进行大异常值剔除的方法，方法的崩溃点为５０％，同时给出了算例，并对初轨精度和剔除门限进行了讨论。 相似文献
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等离子体弧是日冕中的一种基本结构,其高温观测特性意味着它有较高的等离子体压力。本文在二维近似下,讨论了等离子体拱被两个强磁场区域所约束时的平衡。对于较大的等离子体标高,等离子体具有近似圆弧形的结构。通过求出强磁场区域中的磁场位形,可以得到孤立的等离子体拱的平衡状态。由于总压守恒的边界条件是高度非线性的,整个问题是一类非线性的自由边界问题。在近圆弧形近似下,其基态是一维的非线性问题,而相对于基态的偏离是二维的线性问题。这样,整个问题可以给出分析解。 相似文献
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双星轨道拟合是基本天文研究领域的重要内容,其给出的动力学质量、轨道参数具有重要的应用价值.前者是恒星系统动力学研究和恒星物理演化研究必不可少的参量,后者则对提高亮星星表参考架的参考星数密度具有重要意义.但是,该项研究此前普遍采用了一些近似,如切平面的变化与空间的透视效应均被忽略.对上百个含亮子星的双星系统而言,这些近似引起观测量计算的偏差已经超过了当前的观测误差(1 mas).我们以牛顿二体模型为基础,用严格的立体几何关系改进了观测量的计算方法,通过仿真和观测数据验证了方法改进的有效性.拟合的结果表明,模型参数的拟合值和子星的观测量预报均有显著的改进.因此,对于双星,尤其是太阳系邻近的远距双星,改进观测量计算方法是必须的. 相似文献
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Yūki Kubo 《Solar physics》2008,248(1):85-98
This article discusses statistical models for the solar flare interval distribution in individual active regions. We analyzed
solar flare data in 55 active regions that are listed in the Geosynchronous Operational Environmental Satellite (GOES) soft X-ray flare catalog for the years from 1981 to 2005. We discuss some problems with a conventional procedure to
derive probability density functions from any data set and propose a new procedure, which uses the maximum likelihood method
and Akaike Information Criterion (AIC) to objectively compare some competing probability density functions. Previous studies
of the solar flare interval distribution in individual active regions only dealt with constant or time-dependent Poisson process
models, and no other models were discussed. We examine three models – exponential, lognormal, and inverse Gaussian – as competing
models for probability density functions in this study. We found that lognormal and inverse Gaussian models are more likely
models than the exponential model for the solar flare interval distribution in individual active regions. The possible solar
flare mechanisms for the distribution models are briefly mentioned. We also briefly investigated the time dependence of probability
density functions of the solar flare interval distribution and found that some active regions show time dependence for lognormal
and inverse Gaussian distribution functions. The results suggest that solar flares do not occur randomly in time; rather,
solar flare intervals appear to be regulated by solar flare mechanisms. Determining a solar flare interval distribution is
an essential step in probabilistic solar flare forecasting methods in space weather research. We briefly mention a probabilistic
solar flare forecasting method as an application of a solar flare interval distribution analysis. The application of our distribution
analysis to a probabilistic solar flare forecasting method is one of the main objectives of this study. 相似文献
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Recently new calculations for the probability field distribution in plasma generating a new expression for the Debye screening fields was carried out by Martin and Perez (1996). This field is a very accurate solution of the Poisson equation for a point test charge in a plasma described by a uniform charge density at Boltzmann thermal equilibrium. The method that we here present is based mainly on the introduction of this adequate field considering the dependence of the potential with the magnitude of the test charge in the calculus of the distribution. First we find the spectral function F(k) carrying out the Fourier transform of the field which is numerically calculated for each representative value of the variable in k space and then fitting these data in order to get F(k). Thus, after the usual numerical integration on the wave number space d3k, the field strength distribution is achieved. This approximation recovers the Holtsmark distribution in the limit of high temperature, and/or, small densities as also these where 0. As in previous works (Ecker, 1972; Spatschek, 1990) the most probable value of the field decreases as the temperature is reduced, and/or, the density increased. 相似文献
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本文针对晚型星红外辐射的一些模型，讨论相应的拟合方法。对有拱星壳层的晚型星的双黑体模型，给出了具体的拟合方法──线性化方法。最后我们就拟合结果及拟合程序编制方面讨论了线性化方法的优缺点。 相似文献
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If X , which follows a power-law distribution, is observed subject to Gaussian measurement error e , then X + e is distributed as the convolution of the power-law and Gaussian distributions. Maximum-likelihood estimation of the parameters of the two distributions is considered. Large-sample formulae are given for the covariance matrix of the estimated parameters, and implementation of a small-sample method (the jackknife) is also described. Other topics dealt with are tests for goodness of fit of the posited distribution, and tests whether special cases (no measurement errors or an infinite upper limit to the power-law distribution) may be preferred. The application of the methodology is illustrated by fitting convolved distributions to masses of giant molecular clouds in M33 and the Large Magellanic Cloud (LMC), and to H i cloud masses in the LMC. 相似文献
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M. Sallah 《Astrophysics and Space Science》2014,350(1):89-101
The problem of monoenergetic radiative transfer in a finite planar stochastic atmospheric medium with polarized (vector) Rayleigh scattering is proposed. The solution is presented for an arbitrary absorption and scattering cross sections. The extinction function of the medium is assumed to be a continuous random function of position, with fluctuations about the mean taken as Gaussian distributed. The joint probability distribution function of these Gaussian random variables is used to calculate the ensemble-averaged quantities, such as reflectivity and transmissivity, for an arbitrary correlation function. A modified Gaussian probability distribution function is also used to average the solution in order to exclude the probable negative values of the optical variable. Pomraning-Eddington approximation is used, at first, to obtain the deterministic analytical solution for both the total intensity and the difference function used to describe the polarized radiation. The problem is treated with specular reflecting boundaries and angular-dependent externally incident flux upon the medium from one side and with no flux from the other side. For the sake of comparison, two different forms of the weight function, which introduced to force the boundary conditions to be fulfilled, are used. Numerical results of the average reflectivity and average transmissivity are obtained for both Gaussian and modified Gaussian probability density functions at the different degrees of polarization. 相似文献
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We use the spherical evolution approximation to investigate non-linear evolution from the non-Gaussian initial conditions characteristic of the local f nl model. We provide an analytic formula for the non-linearly evolved probability distribution function (PDF) of the dark matter which shows that the underdense tail of the non-linear PDF in the f nl model should differ significantly from that for Gaussian initial conditions. Measurements of the underdense tail in numerical simulations may be affected by discreteness effects, and we use a Poisson counting model to describe this effect. Once this has been accounted, our model is in good quantitative agreement with the simulations. In principle, our calculation is an important first step in programs which seek to reconstruct the shape of the initial PDF from observations of large-scale structures in the Lyα forest and the galaxy distribution at later times. 相似文献
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时序资料的时间窗平滑法及应用 总被引：3，自引：0，他引：3
观测资料的平滑处理，是数据分析中一类重要的常用方法，平滑处理的目的，在于既保留资料中的主要有用信号，又消除或削弱随机误差，本文对密集采样时序资料，提出了时间窗平滑法，并以光谱和光电测量资料为例，通过分析ＰＤＭ技术中拟合曲线的计算，说明了它的性质与应用，与高斯权函数平滑法相比，此方法计算简便，且有更明确的物理意义，与观测值多点合并法相比，有更好的采样一致性和避免损失实际的分辨率，当用于等间距时序资料 相似文献
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We show that the explicit assumption of a chemically inhomogeneous interstellar medium allows a better reproduction of the metallicity distribution of G-dwarfs in the solar neighbourhood. The inhomogeneity is considered by assuming that at any time stars are born with a spread in their metallicities, the spread being a Gaussian in the logarithm of the metallicity around the mean metallicity of that epoch. We show that for various simple models of chemical evolution, the fit to the G-dwarf metallicity curve improves considerably once the above assumption is applied. We show that the parameters obtained from the fitting also give acceptable predictions for the age-metallicity relation. We also find that if we use a G-dwarf metallicity function corrected for the scale height inflation of stars, the conventional models of chemical evolution cannot match the shape of the curve, at least under the instantaneous recycling approximation applied to a chemically homogeneous ISM. Under the inhomogeneous ISM approximation, the predicted shapes are found to be better, though not totally satisfactory. 相似文献
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The maximum entropy method (MEM) of image reconstructtion is discussed in the context of incomplete Fourier information (as
in aperture synthesis). Several current viewpoints on the conceptual foundation of the method are analysed and found to be
unsatisfactory. It is concluded that the MEM is a form of model-fitting, the model being a non-linear transform of a band-limited
function. A whole family of ’entropies’ can be constructed to give reconstructions which (a) are individually unique, (b)
have sharpened peaks and (c) have flattened baselines. The widely discussed 1nB and - B1nB forms of the entropy are particular
cases and lead to Lorentzian and Gaussian shaped peaks respectively. However, they hardly exhaust the possibilities-for example,
B1/2 is equally good.
The two essential features of peak sharpening and baseline flattening are shown to depend on a parameter which can be controlled
by adding a suitable constant to the zero spacing correlation ρ00. This process, called FLOATing, effectively tames much of the unphysical behaviour noted in earlier studies of the MEM. A
numerical scheme for obtaining the MEM reconstruction is described. This incorporates the FLOAT feature and uses the fast
Fourier transform (FFT), requiring about a hundred FFTs for convergence. Using a model brightness distribution, the MEM reconstructions
obtained for different entropies and different values of the resolution parameter are compared. The results substantiate the
theoretically deduced properties of the MEM.
To allow for noise in the data, the least-squares approach has been widely used. It is shown that this method is biased since
it leads to deterministic residuals which do not have a Gaussian distribution. It is suggested that fitting the noisy data
exactly has the advantage of being unbiased even though the noise appears in the final map. A comparison of the strengths
and weaknesses of the MEM and CLEAN suggests that the MEM already has a useful role to play in image reconstruction. 相似文献