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631.
Hisao Nagao 《统计学通讯:理论与方法》2013,42(7):1547-1567
The limiting distributions of jackknife statistics for eigenvalues of a sample covariance matrix are derived under the nonnormal situations. Also the numerical examples are given under normal and nonnormal populations. 相似文献
632.
《统计学通讯:理论与方法》2012,41(3):567-589
AbstractIn this paper, we study a kind of reflected backward stochastic differential equations (BSDEs) whose generators are of quadratic growth in z and linear growth in y. We first give an estimate of solutions to such reflected BSDEs. Then under the condition that the generators are convex with respect to z, we can obtain a comparison theorem, which implies the uniqueness of solutions for this kind of reflected BSDEs. Besides, the assumption of convexity also leads to a stability property in the spirit of above estimate. We further establish the nonlinear Feynman-Kac formula of the related obstacle problems for partial differential equations (PDEs) in our framework. At last, a numerical example is given to illustrate the applications of our theoretical results, as well as its connection with an optimal stopping time problem. 相似文献
633.
《The American statistician》2013,67(3):258-260
In many probability and mathematical statistics courses the probability generating function (PGF) is typically overlooked in favor of the more utilized moment generating function. However, for certain types of random variables, the PGF may be more appealing. For example, sums of independent, non-negative, integer-valued random variables with finite support are easily studied via the PGF. In particular, the exact distribution of the sum can easily be calculated. Several illustrative classroom examples, with varying degrees of difficulty, are presented. All of the examples have been implemented using the R statistical software package. 相似文献
634.
Robert M. Tardiff 《The American statistician》2013,67(1)
Beginning probability students are often confused by the use of Taylor polynomials in the proof of the central limit theorem. This article provides a proof of the central limit theorem based on L'Hospital's rule rather than on Taylor polynomials. 相似文献
635.
C. Asok 《The American statistician》2013,67(3)
Basu (1958) and Raj and Khamis (1958) have shown that in sampling with replacement the average over distinct units possesses lower variance than the average over the entire sample, including repetitions. While Basu proves the result by the use of the Rao-Blackwell theorem, Raj and Khamis prove it by making use of the distribution of the number of distinct units u in the sample, and the proof is quite involved. Here, an elementary algebraic proof is given. 相似文献
636.
The Gauss-Markov (GM) theorem and its many consequences are well known. It has been our experience that graduate students in linear model courses benefit substantially by deriving these consequences, all of which form natural corollaries to the GM theorem. In deriving any one lemma, the student is compelled to reuse many other GM-based lemmas. In this article we present another example of such a lemma that arises in the forward-elimination variable selection procedure. The derivation given is considered to be pedagogically useful. 相似文献
637.
Several statistical applications demand the adoption of models in which the response is binary but the outcomes of different trials exhibit some degree of correlation. Although the independent case is well known and treated even in elementary textbooks, results on correlated Bernoulli trials are hardly found in the literature. Analogues of the binomial and negative binomial distributions are presented in this article when the correlation is of the Markovian type. Probability-generating function, probability mass function, mean, and variance are derived. The analysis allows illustration of a variety of techniques useful in the study of discrete distributions appropriate for second-level probability courses. An example on customer brand switching discussed by Olkin, Glesser, and Derman is presented as illustration. 相似文献
638.
Joel E. Cohen 《The American statistician》2013,67(4):399-404
Taylor's law, which originated in ecology, states that, in sets of measurements of population density, the sample variance is approximately proportional to a power of the sample mean. Taylor's law has been verified for many species ranging from bacterial to human. Here, we show that the variance V(x) and the mean M(x) of the primes not exceeding a real number x obey Taylor's law asymptotically for large x. Specifically, V(x) ~ (1/3)(M(x))2 as x → ∞. This apparently new fact about primes shows that Taylor's law may arise in the absence of biological processes, and that patterns discovered in biological data can suggest novel questions in number theory. If the Hardy-Littlewood twin primes conjecture is true, then the identical Taylor's law holds also for twin primes. Taylor's law holds in both instances because the primes (and the twin primes, given the conjecture) not exceeding x are asymptotically uniformly distributed on the integers in [2, x]. Hence, asymptotically M(x) ~ x/2, V(x) ~ x2/12. Higher-order moments of the primes (twin primes) not exceeding x satisfy a generalized Taylor's law. The 11,078,937 primes and 813,371 twin primes not exceeding 2 × 108 illustrate these results. 相似文献
639.
J.-P Stockis & H. Tong 《Journal of the Royal Statistical Society. Series B, Statistical methodology》1998,60(4):781-798
We have obtained the asymptotic bias and the limiting distribution for the Yule–Walker estimator of the autoregressive parameter under a considerably weaker assumption than that of independence in the noise sequence. Among other things, these suggest robustness of the classical results and throw some light on the use of simulations based on pseudorandom numbers in verifying these results. 相似文献
640.
《Journal of Statistical Computation and Simulation》2012,82(3-4):249-251
Confidence intervals obtained by bootstrap methods and normal approximation are compared, based on output data from terminating and steady-state simulations. Bootstrap intervals are equal or better than normal approximation intervals in actual probability coverages. Furthermore, bootstrap methods capture the skewness in the distribution of outputs and, therefore, are more desirable than normal approximation. 相似文献