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11.
Aaron Childs 《统计学通讯:理论与方法》2013,42(9):1647-1662
In this article we provide a unified framework for solving Dirichlet related probability and waiting time problems. We consider a Pólya sampling scheme in which each time an object is selected, it is put back into the population along with c additional objects of the same type. By considering both fixed sample size and inverse sampling procedures, we unify the Dirichlet I, J, C, and D functions with their hypergeometric counterparts by extending these functions to Pólya sampling. We then use these functions to unify and extend the corresponding expected waiting time results. 相似文献
12.
Rao (1961, 1963) introduced a measure of second order efficiency (s.o.e.) of a best asymptotically normal (BAN) estimator and obtained the s.o.e's of some well known estimators of the parameter of the multinomial family. Koorts (1985) dealt with a calss of BAN estimators and derived the s.o.e, of the estimator belonging to this class. In this paper we derive a general expressiion for the s.o.e. of a BAN estiimator based on its estimating equation. 相似文献
13.
Shulamith T. Gross 《统计学通讯:理论与方法》2013,42(3):1027-1037
Bayes credibility limits for small proportions from stratified and fixed size cluster samples are discussed. Ericson’s (JRSS B (1969)) Beta Binomial and Dirichlet-Multinomial priors are used. Approximate limits that are appropriate for large samples and small proportions are derived in both cases. These allow asymptotic comparisons of the efficacy of stratified and cluster sampling relative to simple random sampling for estimating small proportions. Procedures for the selection of hyper parameters are also presented. 相似文献
14.
《统计学通讯:理论与方法》2013,42(4):847-856
ABSTRACT The randomized response technique is an effective survey method designed to elicit sensitive information while ensuring the privacy of the respondents. In this article, we present some new results on the randomization response model in situations wherein one or two response variables are assumed to follow a multinomial distribution. For a single sensitive question, we use the well-known Hopkins randomization device to derive estimates, both under the assumption of truthful and untruthful responses, and present a technique for making pairwise comparisons. When there are two sensitive questions of interest, we derive a Pearson product moment correlation estimator based on the multinomial model assumption. This estimator may be used to quantify the linear relationship between two variables when multinomial response data are observed according to a randomized-response protocol. 相似文献
15.
This article presents a Bayesian analysis of a multinomial probit model by building on previous work that specified priors on identified parameters. The main contribution of our article is to propose a prior on the covariance matrix of the latent utilities that permits elements of the inverse of the covariance matrix to be identically zero. This allows a parsimonious representation of the covariance matrix when such parsimony exists. The methodology is applied to both simulated and real data, and its ability to obtain more efficient estimators of the covariance matrix and regression coefficients is assessed using simulated data. 相似文献
16.
Hélcio Vieira Jr. Karl Heinz Kienitz Mischel Carmen Neyra Belderrain 《统计学通讯:模拟与计算》2013,42(5):971-980
The two well-known and widely used multinomial selection procedures Bechhofor, Elmaghraby, and Morse (BEM) and all vector comparison (AVC) are critically compared in applications related to simulation optimization problems. Two configurations of population probability distributions in which the best system has the greatest probability p i of yielding the largest value of the performance measure and has or does not have the largest expected performance measure were studied. The numbers achieved by our simulations clearly show that none of the studied procedures outperform the other in all situations. The user must take into consideration the complexity of the simulations and the performance measure probability distribution properties when deciding which procedure to employ. An important discovery was that the AVC does not work in populations in which the best system has the greatest probability p i of yielding the largest value of the performance measure but does not have the largest expected performance measure. 相似文献
17.
《The American statistician》2012,66(4):313-320
ABSTRACTThere is no established procedure for testing for trend with nominal outcomes that would provide both a global hypothesis test and outcome-specific inference. We derive a simple formula for such a test using a weighted sum of Cochran–Armitage test statistics evaluating the trend in each outcome separately. The test is shown to be equivalent to the score test for multinomial logistic regression, however, the new formulation enables the derivation of a sample size formula and multiplicity-adjusted inference for individual outcomes. The proposed methods are implemented in the R package multiCA. 相似文献
18.
19.
Y. K. Tse 《商业与经济统计学杂志》2013,31(1):61-65
A new functional form of the response probability for a qualitative response model is proposed. The new model is flexible enough to avoid the constraint of independence from irrelevant alternatives, which is perceived as a weakness of the multinomial logit model in some applications. It is computationally simpler than the multinomial probit model and is promising for analyzing problems with a moderate number of alternatives. 相似文献
20.
We model the effect of a road safety measure on a set of target sites with a control area for each site, and we suppose that the accident data recorded at each site are classified in different mutually exclusive types. We adopt the before–after technique and we assume that at any one target site the total number of accidents recorded is multinomially distibuted between the periods and types of accidents. In this article, we propose a minorization–majorization (MM) algorithm for obtaining the constrained maximum likelihood estimates of the parameter vector. We compare it with a gradient projection–expectation maximization (GP-EM) algorithm, based on gradient projections. The performance of the algorithms is examined through a simulation study of road safety data. 相似文献