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1.
Random Bernstein Polynomials   总被引:5,自引:0,他引:5  
Random Bernstein polynomials which are also probability distribution functions on the closed unit interval are studied. The probability law of a Bernstein polynomial so defined provides a novel prior on the space of distribution functions on [0, 1] which has full support and can easily select absolutely continuous distribution functions with a continuous and smooth derivative. In particular, the Bernstein polynomial which approximates a Dirichlet process is studied. This may be of interest in Bayesian non-parametric inference. In the second part of the paper, we study the posterior from a Bernstein–Dirichlet prior and suggest a hybrid Monte Carlo approximation of it. The proposed algorithm has some aspects of novelty since the problem under examination has a changing dimension parameter space.  相似文献   
2.
The occurrence of missing data cells precludes a universally correct procedure for performing an analysis of variance. This is illustrated by the use of two computer routines to analyze a 2 × 3 factorial experiment with one missing cell. One of these routines does, however, provide information that may enhance the usefulness of the associated results.  相似文献   
3.
Jen Tang  A.K. Gupta 《Statistics》2013,47(3):379-387
In this paper, WILKS'type-B integral equation is solved in the general form of a series of beta functions and a series of weighted gamma functions as proposed by WALD and BROOKNER 1941. The coefficients in both representations can be obtained by explicit recurrence relartions, therefore the results solve many distributional problems and have the fewest computational difficulties of any representation that has surfaced to date. The radius of convergence of the second series representation is given, whereas the convergence property of the first series representation is given, whereas the convergence property of the first series representation was studied by WALD and Brookner. The exact null distributions of WILKS' statistic A for testing the independence of several groups of variables and of V = -log A are given. The coefficients in all the series representration can be computed recursilvely and hence can be obtained easily with the help of modern computatinal facilities  相似文献   
4.
Functional data analysis (FDA)—the analysis of data that can be considered a set of observed continuous functions—is an increasingly common class of statistical analysis. One of the most widely used FDA methods is the cluster analysis of functional data; however, little work has been done to compare the performance of clustering methods on functional data. In this article, a simulation study compares the performance of four major hierarchical methods for clustering functional data. The simulated data varied in three ways: the nature of the signal functions (periodic, non periodic, or mixed), the amount of noise added to the signal functions, and the pattern of the true cluster sizes. The Rand index was used to compare the performance of each clustering method. As a secondary goal, clustering methods were also compared when the number of clusters has been misspecified. To illustrate the results, a real set of functional data was clustered where the true clustering structure is believed to be known. Comparing the clustering methods for the real data set confirmed the findings of the simulation. This study yields concrete suggestions to future researchers to determine the best method for clustering their functional data.  相似文献   
5.
The study of the dependence between two medical diagnostic tests is an important issue in health research since it can modify the diagnosis and, therefore, the decision regarding a therapeutic treatment for an individual. In many practical situations, the diagnostic procedure includes the use of two tests, with outcomes on a continuous scale. For final classification, usually there is an additional “gold standard” or reference test. Considering binary test responses, we usually assume independence between tests or a joint binary structure for dependence. In this article, we introduce a simulation study assuming two dependent dichotomized tests using two copula function dependence structures in the presence or absence of verification bias. We compare the test parameter estimators obtained under copula structure dependence with those obtained assuming binary dependence or assuming independent tests.  相似文献   
6.
When the method of least squares is used to estimate the parameters in a general model and the generated system of normal equations is linearly dependent, the estimate of the vector of parameters which satisfies the criterion is not unique. However, there exist certain functions of the estimated vector of parameters which are invariant to the least squares solution obtained from the normal equations. We define those invariant functions to be estimable, and present a technique to determine the functions of the parameters which are estimable for the general model. The method results in solving either a linear first order partial differential equation or a system of linear first order partial differential equations corresponding, respectively, to a single or multiple dependency between columns of the Jacobian matrix of the mean of the model. The usual results concerning estimability for linear models are a special case of the general results developed.  相似文献   
7.
In an earlier article (Kulkarni and Paranjape 1984) we proposed a procedure based on Andrews' function plot technique for the quality control of multivariate process. It was shown that this procedure may lead to an erroneous conclusions regarding the status of the process. This article presents an improved method which avoids the above drawback. A heuristic justification is provided to show that the new method is free from the error. Simulation studies are carried out to support the claim. An example is included to illustrate the use of the new technique.  相似文献   
8.
In a series of papers, Kshirsagar (1964, 1971) and McHenry and Kshirsagar (1977), factorize Wilks' A into a number of factors and find the independent null multivariate beta densities of these factors. These factors are the likelihood ratio test criteria for testing the goodness of fit of certain assigned discriminant functions or canonical variables either in the space of independent or dependent variables. Essentially the factors of Wilks' A are the factors of certain multivariate beta distributed matrix or its determinant. The Bartlett decomposition of the underlying multivariate beta distribution into independent factors determines the distribution of these factors. The present paper generalizes Kshirsagar's (1971) normal theory to the elliptically contoured model, and shows that his results are null robust for the elliptically contoured model.  相似文献   
9.
The cosine distribution serves as a very good teaching example for which exact moment properties of extreme order statistics can be expressed in terms of elementary functions. This article presents the limiting joint distribution of the extreme order statistics for the cosine distribution. It is shown that burrows'(1986) result is a special case of the result presented in this article.  相似文献   
10.
We establish the exact expressions of X1/X2 and of X1/(X1+X2), where X1 and X2 are independent beta random variables of the first type, and provide some of their applications, in reliability and availability.  相似文献   
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