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11.
Linda June Davis 《The American statistician》2013,67(2):139-141
Fisher's exact test, difference in proportions, log odds ratio, Pearson's chi-squared, and likelihood ratio are compared as test statistics for testing independence of two dichotomous factors when the associated p values are computed by using the conditional distribution given the marginals. The statistics listed above that can be used for a one-sided alternative give identical p values. For a two-sided alternative, many of the above statistics lead to different p values. The p values are shown to differ only by which tables in the opposite tail from the observed table are considered more extreme than the observed table. 相似文献
12.
Robert E. McCulloch 《The American statistician》2013,67(1):73-75
A very strong relationship between the directed Kullback divergence and the likelihood function emerges simply and naturally in the context of exponential families. The directed Kullback divergence is an information-theoretic measure of the distance from one distribution to another. 相似文献
13.
Fei Li 《统计学通讯:理论与方法》2013,42(8):1184-1206
We define zonal polynomials of quaternion matrix argument and deduce some impor-tant formulae of zonal polynomials and hypergeometric functions of quaternion matrix argument. As an application, we give the distributions of the largest and smallest eigenvalues of a quaternion central Wishart matrix W ~ ?W(n, Σ), respectively. 相似文献
14.
Summary Misclassifications, or noises, in the sampling stage of a Bayesian scheme can seriously affect the values of decision criteria
such as the Bayes Risk and the Expected Value of Sample Information. This problem does not seem to be much addressed in the
existing literature. In this article, using an approach based on hypergeometric functions and numerical computation, we study
the effects of these noises under the two most important loss functions: the quadratic and the absolute value. A numerical
example illustrates these effects in a representative case, using both loss functions, and provides additional insights into
the general problem.
Research partially supported by NSERC grant A 9249 (Canada) and FICU Grant 2000/pas/13. The authors wish to thank colleagues
at the University of Alberta in Edmonton, Canada, for very stimulating discussions, and an anonymous referee for drawing their
attention to three relevant references that have enriched the content of this final version. 相似文献
15.
The exact distribution of a modified Behrens–Fisher statistic is derived. The distribution function is mostly elementary and is simpler than the exact distribution derived by Nel et al. Its practical use (including computationalefficiency and computational convenience) is discussed. 相似文献
16.
Peter Zörnig 《统计学通讯:理论与方法》2014,43(9):1887-1906
We study the distributions of the random variables Sn and Vr related to a sequence of dependent Bernoulli variables, where Sn denotes the number of successes in n trials and Vr the number of trials necessary to obtain r successes. The purpose of this article is twofold: (1) Generalizing some results on the “nature” of the binomial and negative binomial distributions we show that Sn and Vr can follow any prescribed discrete distribution. The corresponding joint distributions of the Bernoulli variables are characterized as the solutions of systems of linear equations. (2) We consider a specific type of dependence of the Bernoulli variables, where the probability of a success depends only on the number of previous successes. We develop some theory based on new closed-form representations for the probability mass functions of Sn and Vr which enable direct computations of the probabilities. 相似文献
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18.
In this paper we provide a comprehensive Bayesian posterior analysis of trend determination in general autoregressive models. Multiple lag autoregressive models with fitted drifts and time trends as well as models that allow for certain types of structural change in the deterministic components are considered. We utilize a modified information matrix-based prior that accommodates stochastic nonstationarity, takes into account the interactions between long-run and short-run dynamics and controls the degree of stochastic nonstationarity permitted. We derive analytic posterior densities for all of the trend determining parameters via the Laplace approximation to multivariate integrals. We also address the sampling properties of our posteriors under alternative data generating processes by simulation methods. We apply our Bayesian techniques to the Nelson-Plosser macroeconomic data and various stock price and dividend data. Contrary to DeJong and Whiteman (1989a,b,c), we do not find that the data overwhelmingly favor the existence of deterministic trends over stochastic trends. In addition, we find evidence supporting Perron's (1989) view that some of the Nelson and Plosser data are best construed as trend stationary with a change in the trend function occurring at 1929. 相似文献
19.
《Journal of Statistical Computation and Simulation》2012,82(7):531-542
In this paper, we present the use of computational aspects in the study of the family of discrete distributions generated by the hypergeometric function 3 F 2, which is a univariate extension of the Gaussian hypergeometric function. These computational techniques allow us to obtain the probability mass function, the mean, the mode in an explicit form as well as the knowledge of the most important properties. We can also obtain a summation result and implement different methods of estimation. Finally, we present an example of an application to real data already fitted by other discrete distributions. 相似文献
20.
Howard Levene 《The American statistician》2013,67(2):71-73
It is demonstrated that important properties of the distribution of runs can be obtained immediately from the hypergeometric distribution for which results are already well-known. 相似文献