共查询到20条相似文献,搜索用时 46 毫秒
1.
《随机性模型》2013,29(2):157-190
In this paper, we establish an explicit form of matrix decompositions for the queue length distributions of the MAP/G/1 queues under multiple and single vacations with N-policy. We show that the vector generating function Y (z) of the queue length at an arbitrary time and X (z) at departures are decomposed into Y (z) = p idle (z)ζ Y (z) and X (z) = p idle (z)ζ X (z) where p idle (z) is the vector generating function of the queue length at an arbitrary epoch at which the server is not in service, and ζ Y (z) and ζ X (z) are unidentified matrix generating functions. 相似文献
2.
《统计学通讯:模拟与计算》2013,42(3):357-373
ABSTRACT This paper studies the asymptotic distribution of the largest eigenvalue of the sample covariance matrix. The multivariate distribution for the population is assumed to be elliptical with finite kurtosis 3κ. An expression as an expectation is obtained for the distribution function of the largest eigenvalue regardless of the multiplicity, m, of the population's largest eigenvalue. The asymptotic distribution function and density function are evaluated numerically for m = 2,3,4,5. The bootstrap of the average of the m largest eigenvalues is shown to be consistent for any underlying distribution with finite fourth-order cumulants. 相似文献
3.
Consider a discrete time Markov chain X(n) denned on {0,1,…} and let P be the transition probability matrix governing X(n). This paper shows that, if a transformed matrix of P is totally positive of order 2, then poj(n) and pio(n) are unimodal with respect to n, where pij(n) = Pr[X(n) = j |X(0) = i]. Furthermore, the modes of poj(n) and pio(n) are non-increasing in j and I, respectively, when additionally P itself is totally positive of order 2. These results are transferred to a class of semi-Markov processes via a uniformization. 相似文献
4.
G. S. Watson 《Australian & New Zealand Journal of Statistics》1984,26(3):272-276
An explicit algorithm is given for constructing a confidence region on the appropriate unit sphere for an eigenvector, given a large sample. It is assumed the eigenvector corresponds to the largest eigenvalue of ExxT, a matrix with distinct eigenvalues, and that the estimation uses n-1S?xixixT. While the theory is generally applicable, the writer has in mind the special case where ∥x∥= 1 i.e. directional data. 相似文献
5.
《统计学通讯:模拟与计算》2013,42(4):963-989
Monte Carlo simulations were done to estimate the means and standard deviations of the characteristic roots of a Wishart matrix which can be used in computing tests of hypotheses concerning multiplicative terms in balanced linear-bilinear (multiplicative) models for an m × n table of data. In this report we extend the previous results (Mandel, 1971; Cornelius, 1980) to r ≤ 199, c ≤ 149 or r ≤ 149, c ≤ 199, where r and c are row and column degrees of freedom, respectively, of the two-way array of residuals (with total degrees of freedom rc) after fitting the linear effects. For 187 combinations of r and c at intervals over this domain, we used 5000 simulations to estimate expectations and standard deviations of the Wishart roots. Using weighted linear regression variable selection techniques, symmetric functions of r and c were obtained for approximating the simulated means and standard deviations. Use of these approximating functions will avoid the need for reference to tables for input to computer programs which require these values for tests of significance of sequentially fitted terms in the analyses of balanced linear-bilinear models. 相似文献
6.
D.B. Jensen 《Australian & New Zealand Journal of Statistics》1972,14(1):10-16
Let S (p×p) have a Wishart distribution -with v degrees of freedom and non-centrality matrix θ= [θjK] (p×p). Define θ0= min {| θjk |}, let θ0→∞, and suppose that | θjK | = 0(θo). Then the limiting form of the standardized non-central distribution, as θ while n? remains fixed, is a multivariate Gaussian distribution. This result in turn is used to obtain known asymptotic properties of multivariate chi-square and Rayleigh distributions under somewhat weaker conditions. 相似文献
7.
We discuss the case of the multivariate linear model Y = XB + E with Y an (n × p) matrix, and so on, when there are missing observations in the Y matrix in a so-called nested pattern. We propose an analysis that arises by incorporating the predictive density of the missing observations in determining the posterior distribution of B, and its mean and variance matrix. This involves us with matric-T variables. The resulting analysis is illustrated with some Canadian economic data. 相似文献
8.
ON THE NUMBER OF RECORDS NEAR THE MAXIMUM 总被引:3,自引:0,他引:3
Recent work has considered properties of the number of observations Xj, independently drawn from a discrete law, which equal the sample maximum X(n) The natural analogue for continuous laws is the number Kn(a) of observations in the interval (X(n)–a, X(n)], where a > 0. This paper derives general expressions for the law, first moment, and probability generating function of Kn(a), mentioning examples where evaluations can be given. It seeks limit laws for n→ and finds a central limit result when a is fixed and the population law has a finite right extremity. Whenever the population law is attracted to an extremal law, a limit theorem can be found by letting a depend on n in an appropriate manner; thus the limit law is geometric when the extremal law is the Gumbel type. With these results, the paper obtains limit laws for ‘top end’ spacings X(n) - X(n-j) with j fixed. 相似文献
9.
《随机性模型》2013,29(3):387-424
This paper considers a single server queue that handles arrivals from N classes of customers on a non-preemptive priority basis. Each of the N classes of customers features arrivals from a Poisson process at rate λ i and class-dependent phase type service. To analyze the queue length and waiting time processes of this queue, we derive a matrix geometric solution for the stationary distribution of the underlying Markov chain. A defining characteristic of the paper is the fact that the number of distinct states represented within the sub-level is countably infinite, rather than finite as is usually assumed. Among the results we obtain in the two-priority case are tractable algorithms for the computation of both the joint distribution for the number of customers present and the marginal distribution of low-priority customers, and an explicit solution for the marginal distribution of the number of high-priority customers. This explicit solution can be expressed completely in terms of the arrival rates and parameters of the two service time distributions. These results are followed by algorithms for the stationary waiting time distributions for high- and low-priority customers. We then address the case of an arbitrary number of priority classes, which we solve by relating it to an equivalent three-priority queue. Numerical examples are also presented. 相似文献
10.
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
11.
S. Stylianou 《统计学通讯:理论与方法》2013,42(10):1776-1784
A conference matrix is a square matrix C with zeros on the diagonal and ±1s off the diagonal, such that C T C = CC T = (n ? 1)I, where I is the identity matrix. Conference matrices are an important class of combinatorial designs due to their many applications in several fields of science, including statistical-experimental designs, telecommunications, elliptic geometry, and more. In this article, conference matrices and their full foldover design are combined together to obtain an alternative method for screening active factors in complicated problems. This method provides a model-independent estimate of the set of active factors and also gives a linearity test for the underlying model. 相似文献
12.
James H. Goodnight 《The American statistician》2013,67(3):149-158
13.
《统计学通讯:模拟与计算》2013,42(4):717-741
In the study of the stochastic behaviour of the lifetime of an element as a function of its length, it is often observed that the failure time (or lifetime) decreases as the length increases. In probabilistic terms, such an idea can be expressed as follows. Let T be the lifetime of a specimen of length x, so the survival function, which denotes the probability that an element of length x survives till time t, will be given by ST (t, x) = P(T > t/α(x), where α(x) is a monotonically decreasing function. In particular, it is often assumed that T has a Weibull distribution. In this paper, we propose a generalization of this Weibull model by assuming that the distribution of T is Generalized gamma (GG). Since the GG model contains the Weibull, Gamma and Lognormal models as special and limiting cases, a GG regression model is an appropriate tool for describing the size effect on the lifetime and for selecting among the embedded models. Maximum likelihood estimates are obtained for the GG regression model with α(x) = cxb . As a special case this provide an alternative to the usual approach to estimation for the GG distribution which involves reparametrization. Related parametric inference issues are addressed and illustrated using two experimental data sets. Some discussion of censored data is also provided. 相似文献
14.
《Journal of Statistical Computation and Simulation》2012,82(11):1065-1076
Sampling the correlation matrix (R) plays an important role in statistical inference for correlated models. There are two main constraints on a correlation matrix: positive definiteness and fixed diagonal elements. These constraints make sampling R difficult. In this paper, an efficient generalized parameter expanded re-parametrization and Metropolis-Hastings (GPX-RPMH) algorithm for sampling a correlation matrix is proposed. Drawing all components of R simultaneously from its full conditional distribution is realized by first drawing a covariance matrix from the derived parameter expanded candidate density (PXCD), and then translating it back to a correlation matrix and accepting it according to a Metropolis-Hastings (M-H) acceptance rate. The mixing rate in the M-H step can be adjusted through a class of tuning parameters embedded in the generalized candidate prior (GCP), which is chosen for R to derive the PXCD. This algorithm is illustrated using multivariate regression (MVR) models and a simulation study shows that the performance of the GPX-RPMH algorithm is more efficient than that of other methods. 相似文献
15.
In this paper, we consider the asymptotic distributions of functionals of the sample covariance matrix and the sample mean vector obtained under the assumption that the matrix of observations has a matrix‐variate location mixture of normal distributions. The central limit theorem is derived for the product of the sample covariance matrix and the sample mean vector. Moreover, we consider the product of the inverse sample covariance matrix and the mean vector for which the central limit theorem is established as well. All results are obtained under the large‐dimensional asymptotic regime, where the dimension p and the sample size n approach infinity such that p/n→c ∈ [0, + ∞) when the sample covariance matrix does not need to be invertible and p/n→c ∈ [0,1) otherwise. 相似文献
16.
The efficiency of a sequential test is related to the “importance” of the trials within the test. This relationship is used to find the optimal test for selecting the greater of two binomial probabilities, pα and pb, namely, the stopping rule is “gambler's ruin” and the optimal discipline when pα+pb≤ 1 (≥ 1) is play-the-winner (loser), i.e. an α-trial which results in a success is followed by an α-trial (b-trial) whereas an α-trial which results in a failure is followed by α b-trid (α-trial) and correspondingly for b-trials. 相似文献
17.
This paper introduces a robust biplot which is related to multivariate M-estimates. The n × p data matrix is first considered as a sample of size n from some p-variate population, and robust M-estimates of the population location vector and scatter matrix are calculated. In the construction of the biplot, each row of the data matrix is assigned a weight determined in the preliminary robust estimation. In a robust biplot, one can plot the variables in order to represent characteristics of the robust variance-covariance matrix: the length of the vector representing a variable is proportional to its robust standard deviation, while the cosine of the angle between two variables is approximately equal to their robust correlation. The proposed biplot also permits a meaningful representation of the variables in a robust principal-component analysis. The discrepancies between least-squares and robust biplots are illustrated in an example. 相似文献
18.
G. J. Mclachlan 《Australian & New Zealand Journal of Statistics》1973,15(3):210-214
When a sample discriminant function is computed, it is desired to estimate the error rate using this function. This is often done by computing G(-D/2), where G is the cumulative normal distribution and D2 is the estimated Mahalanobis' distance. In this paper an asymptotic expansion of the expectation of G(-D/2) is derived and is compared with existing Monte Carlo estimates. The asymptotic bias of G(-D/2) is derived also and the well-known practical result that G(-D/2) gives too favourable an estimate of the true error rate 相似文献
19.
Let Sp × p have a Wishart distribution with parameter matrix Σ and n degrees of freedom. We consider here the problem of estimating the precision matrix Σ?1 under the loss functions L1(σ) tr (σ) - log |σ| and L2(σ) = tr (σ). James-Stein-type estimators have been derived for an arbitrary p. We also obtain an orthogonal invariant and a diagonal invariant minimax estimator under both loss functions. A Monte-Carlo simulation study indicates that the risk improvement of the orthogonal invariant estimators over the James-Stein type estimators, the Haff (1979) estimator, and the “testimator” given by Sinha and Ghosh (1987) is substantial. 相似文献