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71.
72.
Unfortunately many of the numerous algorithms for computing the comulative distribution function (cdf) and noncentrality parameter
of the noncentral F and beta distributions can produce completely incorrect results as demonstrated in the paper by examples. Existing algorithms
are scrutinized and those parts that involve numerical difficulties are identified. As a result, a pseudo code is presented
in which all the known numerical problems are resolved. This pseudo code can be easily implemented in programming language
C or FORTRAN without understanding the complicated mathematical background.
Symbolic evaluation of a finite and closed formula is proposed to compute exact cdf values. This approach makes it possible
to check quickly and reliably the values returned by professional statistical packages over an extraordinarily wide parameter
range without any programming knowledge.
This research was motivated by the fact that a very useful table for calculating the size of detectable effects for ANOVA
tables contains suspect values in the region of large noncentrality parameter values compared to the values obtained by Patnaik’s
2-moment central-F approximation. The cause is identified and the corrected form of the table for ANOVA purposes is given. The accuracy of the
approximations to the noncentral-F distribution is also discussed.
The authors wish to thank Mr. Richárd Király for his preliminary work. The authors are grateful to the Editor and Associate
Editor of STCO and the unknown reviewers for their helpful suggestions. 相似文献
73.
Mohammad Azhar Hussain 《Journal of Economic Inequality》2009,7(3):207-223
This study looks at polarization and its components’ sensitivity to assumptions about equivalence scales, income definition,
ethical income distribution parameters, and the income accounting period. A representative sample of Danish individual incomes
from 1984 to 2002 is utilised. Results show that polarization has increased over time, regardless of the applied measure,
when the last part of the period is compared to the first part of the period; primary causes being increased inequality (alienation)
and faster income growth among high incomes relative to those in the middle of the distribution. Increasing the accounting
period confirms the reduction in inequality found for shorter periods, but polarization is virtually unchanged, because income
group identification increases. Applying different equivalence scales does not change polarization ranking for different years,
but identification ranks are affected. The welfare state considerably reduces income polarization and inequality, but at the
expense of some more identification.
相似文献
74.
《统计学通讯:理论与方法》2013,42(3):397-405
In this article, we present some tests for Exponentiality against Gamma alternatives by using normalized waiting times. The test is constructed by using a quadratic form. The asymptotic distribution of the proposed test is derived. The power of the test is computed through Monte Carlo simulation and is compared with Linhart (1965) test, Bain and Engelhardt (1975) test and Keating et al. (1990) test. 相似文献
75.
P.C. Consul 《统计学通讯:理论与方法》2013,42(8):3051-3068
A new discrete distribution defined over all the positive integers and with the name of Geeta distribution is described. It is L-shaped like the logarithmic series distribution, Yule distribution and the discrete Pareto distribution but is far more versatile than them as it has two parameters. It belongs to the classes of location parameter distributions, modified power series distributions, Lagrange series distributions and exponential distributions. Its mean fi, variance a2 and two recurrence formulae for higher central moments are obtained. Convolution theorem and variations in the model with changes in the parameters have been considered. ML estimators, MVU estimators and estimators based of mean and variance and on mean and first frequency have been derived. 相似文献
76.
Gabriele Brondino 《统计学通讯:模拟与计算》2013,42(2):407-417
The standard tensile test is one of the most frequent tools performed for the evaluation of mechanical properties of metals. An empirical model proposed by Ramberg and Osgood fits the tensile test data using a nonlinear model for the strain in terms of the stress. It is an Error-In-Variables (EIV) model because of the uncertainty affecting both strain and stress measurement instruments. The SIMEX, a simulation-based method for the estimation of model parameters, is powerful in order to reduce bias due to the measurement error in EIV models. The plan of this article is the following. In Sec. 2, we introduce the Ramberg–Osgood model and another reparametrization according to different assumptions on the independent variable. In Sec. 3, there is a summary of SIMEX method for the case at hand. Section 4 is a comparison between SIMEX and others estimating methods in order to highlight the peculiarities of the different approaches. In the last section, there are some concluding remarks. 相似文献
77.
Homoscedastic and heteroscedastic Gaussian mixtures differ in the constraints placed on the covariance matrices of the mixture components. A new mixture, called herein a strophoscedastic mixture, is defined by a new constraint, This constraint requires the matrices to be identical under orthogonal trans¬formations, where different transformations are allowed for different matrices. It is shown that the M-step of the EM method for estimating the parameters of strophoscedastic mixtures from sample data is explicitly solvable using singular value decompositions. Consequently, the EM-based maximum likelihood estimation algorithm is as easily implemented for strophoscedastic mixtures as it is for homoscedastic and heteroscedastic mixtures. An example of a “noisy” Archimedian spiral is presented. 相似文献
78.
This paper extends Lindley's measure of average information to the linear model, E(Y∣ß) = Xß. An expression which quantifies the average amount of information provided by the nxl vector of observations Y about the pxl vector of coefficient parameters ß will be derived. The effect of the structure of the regressor matrix, X, on the information measure is discussed. An information theoretic optimal design is characterized. Some applications are suggested. 相似文献
79.
In teaching the development of uniformly most powerful unbiased (UMPU) tests, one rarely discusses the performance of alternative biased tests. It is shown, through the comparison of two independent Bernoulli proportions, that a biased test (the Z test) can be more powerful than the UMPU test (Fisher's exact test—randomized) in a large region of the alternative parameter space. A more general example is also given. 相似文献
80.
《Journal of Statistical Computation and Simulation》2012,82(1-4):261-270
Sensitivity analysis of air scattered neutron dose at several distances from a particle accelerator with respect to shield thickness and neutron yield distributions has been carried out. We illustrate the successful use of Response Surface Methodology in studying the behaviour of the sensitivity coefficients for main effects and interaction terms. A comparison of the full six factor design and the orthogonal Central Composite Design has been made. The overhead shield is found to be the most sensitive parameter followed by the high energy part of the neutron energy distribution. 相似文献