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31.
Weighted distributions (univariate and bivariate) have received widespread attention over the last two decades because of their flexibility for analyzing skewed data. In this article, we propose an alternative method to construct a new family of bivariate and multivariate weighted distributions. For illustrative purposes, some examples of the proposed method are presented. Several structural properties of the bivariate weighted distributions including marginal distributions together with distributions of the minimum and maximum, evaluation of the reliability parameter, and verification of total positivity of order two are also presented. In addition, we provide some multivariate extensions of the proposed models. A real-life data set is used to show the applicability of these bivariate weighted distributions. 相似文献
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33.
Shin S. Ikeda 《统计学通讯:理论与方法》2017,46(19):9377-9387
A gap in the proof of a non stationary mixingale invariance principle is identified and fixed by introducing a skipped subsampling of a partial sum process and letting the skipped interval vanish asymptotically at an appropriate rate as the sample size increases. The corrected proof produces a mixingale limit theorem in the form of a mixing convergence in law, occurring jointly with the stable convergence in law for the same σ-field relative to which they are stable and mixing. The applicability of established results to a high-frequency estimation of the quadratic variation of financial price process is discussed. 相似文献
34.
Laleh Tafakori A. R. Soltani 《Journal of Statistical Computation and Simulation》2017,87(9):1901-1910
An interesting class of continuous distributions, called Cauchy-type mixture, with potential applications in modelling erratic phenomena is introduced by Soltani and Tafakori [A class of continuous kernels and Cauchy type heavy tail distributions. Statist Probab Lett. 2013;83:1018–1027]. In this work, we provide more insights into the Cauchy-type mixture distributions, involving certain characterizations, connections with the generalized Linnik distributions and the class of discrete distributions induced by stable laws. We also prove that the Laplace transform of Cauchy-type mixture distributions when normalized by constant terms become as a density functions in terms of distributional conjugate property. 相似文献
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36.
Partially linear models (PLMs) are an important tool in modelling economic and biometric data and are considered as a flexible generalization of the linear model by including a nonparametric component of some covariate into the linear predictor. Usually, the error component is assumed to follow a normal distribution. However, the theory and application (through simulation or experimentation) often generate a great amount of data sets that are skewed. The objective of this paper is to extend the PLMs allowing the errors to follow a skew-normal distribution [A. Azzalini, A class of distributions which includes the normal ones, Scand. J. Statist. 12 (1985), pp. 171–178], increasing the flexibility of the model. In particular, we develop the expectation-maximization (EM) algorithm for linear regression models and diagnostic analysis via local influence as well as generalized leverage, following [H. Zhu and S. Lee, Local influence for incomplete-data models, J. R. Stat. Soc. Ser. B 63 (2001), pp. 111–126]. A simulation study is also conducted to evaluate the efficiency of the EM algorithm. Finally, a suitable transformation is applied in a data set on ragweed pollen concentration in order to fit PLMs under asymmetric distributions. An illustrative comparison is performed between normal and skew-normal errors. 相似文献
37.
Some goodness-of-fit procedures for the Cauchy distribution are presented. The power comparisons indicate that the new tests possess good performances among the competitors, especially against symmetric alternatives. A financial data set is analyzed for illustration. 相似文献
38.
Marco Barnabani 《统计学通讯:模拟与计算》2017,46(1):331-343
In general, the exact distribution of a convolution of independent gamma random variables is quite complicated and does not admit a closed form. Of all the distributions proposed, the gamma-series representation of Moschopoulos (1985) is relatively simple to implement but for particular combinations of scale and/or shape parameters the computation of the weights of the series can result in complications with too much time consuming to allow a large-scale application. Recently, a compact random parameter representation of the convolution has been proposed by Vellaisamy and Upadhye (2009) and it allows to give an exact interpretation to the weights of the series. They describe an infinite discrete probability distribution. This result suggested to approximate Moschopoulos’s expression looking for an approximating theoretical discrete distribution for the weights of the series. More precisely, we propose a general negative binomial distribution. The result is an “excellent” approximation, fast and simple to implement for any parameter combination. 相似文献
39.
The ordinary-G class of distributions is defined to have the cumulative distribution function (cdf) as the value of the cdf of the ordinary distribution F whose range is the unit interval at G, that is, F(G), and it generalizes the ordinary distribution. In this work, we consider the standard two-sided power distribution to define other classes like the beta-G and the Kumaraswamy-G classes. We extend the idea of two-sidedness to other ordinary distributions like normal. After studying the basic properties of the new class in general setting, we consider the two-sided generalized normal distribution with maximum likelihood estimation procedure. 相似文献
40.
The forecasting of sales in a company is one of the crucial challenges that must be faced. Nowadays, there is a large spectrum of methods that enable making reliable forecasts. However, sometimes the nature of time series excludes many well-known and widely used forecasting methods (e.g., econometric models). Therefore, the authors decided to forecast on the basis of a seasonally adjusted median of selected probability distributions. The obtained forecasts were verified by means of distributions of the Theil U2 coefficient and unbiasedness coefficient. 相似文献