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51.
R. Willink 《统计学通讯:理论与方法》2013,42(1):170-176
A single parametric form is given for the symmetric distributions in the Pearson system with finite variance. In effect, these are Student's t-distributions with ν > 2 and all centered symmetric beta distributions. A different parametrization allows the inclusion of the t-distributions with ν ≤2 at the expense of symmetric beta distributions with a low shape parameter. 相似文献
52.
Elizabeth H. Payne Mulugeta Gebregziabher James W. Hardin Viswanathan Ramakrishnan Leonard E. Egede 《统计学通讯:模拟与计算》2018,47(6):1722-1738
Overdispersion is a problem encountered in the analysis of count data that can lead to invalid inference if unaddressed. Decision about whether data are overdispersed is often reached by checking whether the ratio of the Pearson chi-square statistic to its degrees of freedom is greater than one; however, there is currently no fixed threshold for declaring the need for statistical intervention. We consider simulated cross-sectional and longitudinal datasets containing varying magnitudes of overdispersion caused by outliers or zero inflation, as well as real datasets, to determine an appropriate threshold value of this statistic which indicates when overdispersion should be addressed. 相似文献
53.
《Journal of Statistical Computation and Simulation》2012,82(4):411-425
In this paper, we give matrix formulae of order 𝒪(n ?1), where n is the sample size, for the first two moments of Pearson residuals in exponential family nonlinear regression models [G.M. Cordeiro and G.A. Paula, Improved likelihood ratio statistic for exponential family nonlinear models, Biometrika 76 (1989), pp. 93–100.]. The formulae are applicable to many regression models in common use and generalize the results by Cordeiro [G.M. Cordeiro, On Pearson's residuals in generalized linear models, Statist. Prob. Lett. 66 (2004), pp. 213–219.] and Cook and Tsai [R.D. Cook and C.L. Tsai, Residuals in nonlinear regression, Biometrika 72(1985), pp. 23–29.]. We suggest adjusted Pearson residuals for these models having, to this order, the expected value zero and variance one. We show that the adjusted Pearson residuals can be easily computed by weighted linear regressions. Some numerical results from simulations indicate that the adjusted Pearson residuals are better approximated by the standard normal distribution than the Pearson residuals. 相似文献
54.
This article considers the uncertainty of a proportion based on a stratified random sample of a small population. Using the hypergeometric distribution, a Clopper–Pearson type upper confidence bound is presented. Another frequentist approach that uses the estimated variance of the proportion estimator is also considered as well as a Bayesian alternative. These methods are demonstrated with an illustrative example. Some aspects of planning, that is, the impact of specified strata sample sizes, on uncertainty are studied through a simulation study. 相似文献
55.
In the present note, we study an extended class of Pearson system of distributions in the context of reliability. It is shown
that the proposed class of models can be characterized by a relatioaship between the failure rate and the conditional moments.
Further, we develop a procedure to identify an increasing (decreasing) failure rate model in the generalized Pearson system. 相似文献
56.
We consider the problem of parameter estimation for an ergodic diffusion with reciprocal gamma invariant distribution. Spectral decomposition of the transition density of such a Markov process is presented in terms of a finite number of discrete eigenfunctions (Bessel polynomials) and eigenfunctions related to a continuous part of the spectrum of the negative infinitesimal generator of reciprocal gamma diffusion. Consistency and asymptotical normality of proposed estimators are presented. Based on the Stein equation for reciprocal gamma diffusion and Bessel polynomials, the hypothesis testing procedure is considered. 相似文献
57.
Abstract. The Pearson diffusions form a flexible class of diffusions defined by having linear drift and quadratic squared diffusion coefficient. It is demonstrated that for this class explicit statistical inference is feasible. A complete model classification is presented for the ergodic Pearson diffusions. The class of stationary distributions equals the full Pearson system of distributions. Well-known instances are the Ornstein–Uhlenbeck processes and the square root (CIR) processes. Also diffusions with heavy-tailed and skew marginals are included. Explicit formulae for the conditional moments and the polynomial eigenfunctions are derived. Explicit optimal martingale estimating functions are found. The discussion covers GMM, quasi-likelihood, non-linear weighted least squares estimation and likelihood inference too. The analytical tractability is inherited by transformed Pearson diffusions, integrated Pearson diffusions, sums of Pearson diffusions and Pearson stochastic volatility models. For the non-Markov models, explicit optimal prediction-based estimating functions are found. The estimators are shown to be consistent and asymptotically normal. 相似文献
58.
The g and h family of distributions, introduced by J.W. Tukey, is generated by a single transformation of the standard normal which allows for symmetry and heavier tails. Selected percentage points are tabulated, and a closed-form solution for the moments, when they exist, is found. A comparison is made with the Pearson system of distributions. The g and h distributions cover most of the Pearson family to an adequate approximation, when the first four moments exist, and also generate a variety of other types of distributions. Selected distributions graphically illustrate the great variety of possible shapes. 相似文献
59.
Eugene D. Gallagher 《The American statistician》2020,74(3):301-306
AbstractQuetelet’s data on Scottish chest girths are analyzed with eight normality tests. In contrast to Quetelet’s conclusion that the data are fit well by what is now known as the normal distribution, six of eight normality tests provide strong evidence that the chest circumferences are not normally distributed. Using corrected chest circumferences from Stigler, the χ2 test no longer provides strong evidence against normality, but five commonly used normality tests do. The D’Agostino–Pearson K2 and Jarque–Bera tests, based only on skewness and kurtosis, find that both Quetelet’s original data and the Stigler-corrected data are consistent with the hypothesis of normality. The major reason causing most normality tests to produce low p-values, indicating that Quetelet’s data are not normally distributed, is that the chest circumferences were reported in whole inches and rounding of large numbers of observations can produce many tied values that strongly affect most normality tests. Users should be cautious using many standard normality tests if data have ties, are rounded, and the ratio of the standard deviation to rounding interval is small. 相似文献
60.
MRBP tests were proposed by Mielke and Iyer (1982) to analyze multivariate data for the randomized block design, based on permutation procedures. They obtained the first three exact moments of the MRBP test statistic to approximate its permutation distribution. Tracy and Khan (1991) derived its fourth exact moment, to obtain a better approximating distribution, when there are four or more treatments. In this paper we obtain the fourth exact moment when the number of treatments is less than four. 相似文献