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1.
An obvious strategy for obtaining a Doptimal foldover design for p factors at two levels each in 2N runs is to fold a Doptimal main effects plan. We show that this strategy works except when N = 4t + 2 and s is even In that case there are two different classes of D-optimal main effects plans with N runs that have the same determinant. However folding them gives two different values foi the D-optimality criteiion One set of designs is D-optimal The other is not.  相似文献   

2.
3.
We study a system of two non-identical and separate M/M/1/? queues with capacities (buffers) C1 < ∞ and C2 = ∞, respectively, served by a single server that alternates between the queues. The server’s switching policy is threshold-based, and, in contrast to other threshold models, is determined by the state of the queue that is not being served. That is, when neither queue is empty while the server attends Qi (i = 1, 2), the server switches to the other queue as soon as the latter reaches its threshold. When a served queue becomes empty we consider two switching scenarios: (i) Work-Conserving, and (ii) Non-Work-Conserving. We analyze the two scenarios using Matrix Geometric methods and obtain explicitly the rate matrix R, where its entries are given in terms of the roots of the determinants of two underlying matrices. Numerical examples are presented and extreme cases are investigated.  相似文献   

4.
For two independent populations X and Y we develop the empirical distribution function estimator for the difference of order statistics of the form X (i)Y (j). The key practical application for this estimator pertains to inference between quantiles from two independent populations.  相似文献   

5.
In this article, a system that consists of n independent components each having two dependent subcomponents (Ai, Bi), i = 1, …, n is considered. The system is assumed to compose of components that have two correlated subcomponents (Ai, Bi), and functions iff both systems of subcomponents A1, A2, …, An and B1, B2, …, Bn work under certain structural rules. The expressions for reliability and mean time to failure of such systems are obtained. A sufficient condition to compare two systems of bivariate components in terms of stochastic ordering is also presented.  相似文献   

6.
The least-squares estimate θn = Xn+yn of the parameter θ in the linear model Yn = Xnθ + ?n may not be consistent, but there may be directions u such that un tends to u'θ in some sense. This set of directions u has been characterized in two different papers: Drygas (1976) and Wu (1980). The conditions for consistency appear to be different in the two papers. The purpose of this note is to show that the two conditions are equivalent and that they both show that the consistent directions depend upon the geometry of the row vectors vi, i = 1,…, n, of Xn with respect to the direction u.  相似文献   

7.
Let f(x) and g(x) denote two probability density functions and g(x)≠0. There are two ways to estimate the density ratio f(x)/g(x). One is to estimate f(x) and g(x) first and then the ratio, the other is to estimate f(x)/g(x) directly. In this paper, we derive asymptotic mean square errors and central limit theorems for both estimators.  相似文献   

8.
Multivariate combination-based permutation tests have been widely used in many complex problems. In this paper we focus on the equipower property, derived directly from the finite-sample consistency property, and we analyze the impact of the dependency structure on the combined tests. At first, we consider the finite-sample consistency property which assumes that sample sizes are fixed (and possibly small) and considers on each subject a large number of informative variables. Moreover, since permutation test statistics do not require to be standardized, we need not assume that data are homoscedastic in the alternative. The equipower property is then derived from these two notions: consider the unconditional permutation power of a test statistic T for fixed sample sizes, with V ? 2 independent and identically distributed variables and fixed effect δ, calculated in two ways: (i) by considering two V-dimensional samples sized m1 and m2, respectively; (ii) by considering two unidimensional samples sized n1 = Vm1 and n2 = Vm2, respectively. Since the unconditional power essentially depends on the non centrality induced by T, and two ways are provided with exactly the same likelihood and the same non centrality, we show that they are provided with the same power function, at least approximately. As regards both investigating the equipower property and the power behavior in presence of correlation we performed an extensive simulation study.  相似文献   

9.
Let X 1, X 2be two independent Poisson random variables with means θ 1and θ 2respectively. Assume 0 ≤ θ 1θ 2 ≤ ∞. The problem is estimation of the ordered parameters which has received considerable attention in statistical literature during the last two decades, In this paper the main portion of the study is devoted to the problem of estimating the smallest of the two ordered Poisson means, when it is known which population corresponds to each mean under the entropy loss function. An extension of the problem to the k-ordered Poisson means is also discussed.  相似文献   

10.
A self-contained FORTRAN subroutine is provided which computes factors for Wald-Wolfowitz type tolerance limits allowing arbitrary combinations of sample size n and degrees of freedom ν. The exact calculations from our program reveal inadequacies of two existing approximations, especially when ν ? n. Numerous applications where νn ? 1 are cited; two of these are discussed and illustrated.  相似文献   

11.
This article deals with the topic of optimal allocation of two standby redundancies in a two-component series/parallel system. There are two original components C1 and C2 which can be used to construct a series/parallel system, and two spares R1 (same as C1) and R2 (different from both C1 and C2) at hand with them being standby redundancies so as to enhance the reliability level of the system. The goal for an engineer is to seek after the optimal allocation policy in this framework. It is shown that, for the series structure, the engineer should allocate R2 to C1 and R1 to C2 provided that C1 (or R1) performs either the best or worst among all the units; otherwise, the allocation policy should be reversed. For the parallel structure, the optimal allocation strategy is just opposed to that of series case. We also provide some numerical examples for illustrating the theoretical results.  相似文献   

12.
Systematic patterns are revealed when sequences of pseudo-random uniform deviates are generated from multiplicative congruential generators. If the initial seeds, x 0 and y 0, for two such sequences are related by y 0 = (n 1/n 2)x 0, where n 1 and n 2 are relatively prime, positive integers, then an approximate argument suggests that the asymptotic correlation coefficient between corresponding members of the two sequences is (n 1 n 2)–1. This unsettling phenomenon is discussed in the context of related, existing literature.  相似文献   

13.
In multiple linear regression analysis each lower-dimensional subspace L of a known linear subspace M of ? n corresponds to a non empty subset of the columns of the regressor matrix. For a fixed subspace L, the C p statistic is an unbiased estimator of the mean square error if the projection of the response vector onto L is used to estimate the expected response. In this article, we consider two truncated versions of the C p statistic that can also be used to estimate this mean square error. The C p statistic and its truncated versions are compared in two example data sets, illustrating that use of the truncated versions may result in models different from those selected by standard C p .  相似文献   

14.
Recent papers by Professor T. Pham-Gia derived distributions of sums, products and ratios of independent beta random variables. In this paper, we extend professor Pham-Gia's results when X 1 and X 2 are independent random variables distributed according to two generalized beta distributions. For each of these distributions, we derive exact expressions for the densities of S=X 1+X 2, D=X 1X 2, P=X 1 X 2, and R=X 2/X 1. The expressions turn out to involve the incomplete beta function as well as the hypergeometric functions of one and two variables.  相似文献   

15.
Let U and V be two symmetric (about zero) random variables with U + V symmetric about C; here C is a constant. It is easy to see that if U and V are mutually independent, or if both U and V satisfy the weak law of large numbers, then C = 0. So, intuitively, we would suspect that C = 0 in general. However, we show that there exist two random variables U and V symmetric about 0 with U + V symmetric about C ≠ 0 The example given is closely related to one given by Alejandro D. De Acosta in another context.  相似文献   

16.
The Generalized Lorenz dominance can be used to take account of differences in mean income as well as income inequality in case of two income distributions possessing unequal means. Asymptotically distribution-free and consistent tests have been proposed for comparing two generalized Lorenz curves in the whole interval [p 1, p 2] where 0 < p 1 < p 2 < 1. Size and power of the test has been derived.  相似文献   

17.
ABSTRACT

In this article, we consider the estimation of R = P(Y < X), when Y and X are two independent three-parameter Lindley (LI) random variables. On the basis of two independent samples, the modified maximum likelihood estimator along its asymptotic behavior and conditional likelihood-based estimator are used to estimate R. We also propose sample-based estimate of R and the associated credible interval based on importance sampling procedure. A real life data set involving the times to breakdown of an insulating fluid is presented and analyzed for illustrative purposes.  相似文献   

18.
This paper investigates two “non-exact” t-type tests, t( k2) and t(k2), of the individual coefficients of a linear regression model, based on two ordinary ridge estimators. The reported results are built on a simulation study covering 84 different models. For models with large standard errors, the ridge-based t-tests have correct levels with considerable gain in powers over those of the least squares t-test, t(0). For models with small standard errors, t(k1) is found to be liberal and is not safe to use while, t(k2) is found to slightly exceed the nominal level in few cases. When tie two ridge tests art: not winners, the results indicate that they don't loose much against t(0).  相似文献   

19.
In the formula of the McNemar test, a test on 2 × 2 classification tables with pairs of data, only the two categories A and D, which represent changes, are included; the retained parts B and C, which represent concordant responses, are not considered. Generally, it would be more reasonable for the significance of the changes to depend not only on A and D, but also on B and C, or on the sample size, n. To develop the test, two formulae, based on A, D, and n, and on A, D, B, C, and n, respectively, are proposed.  相似文献   

20.
A Gaussian copula is widely used to define correlated random variables. To obtain a prescribed Pearson correlation coefficient of ρx between two random variables with given marginal distributions, the correlation coefficient ρz between two standard normal variables in the copula must take a specific value which satisfies an integral equation that links ρx to ρz. In a few cases, this equation has an explicit solution, but in other cases it must be solved numerically. This paper attempts to address this issue. If two continuous random variables are involved, the marginal transformation is approximated by a weighted sum of Hermite polynomials; via Mehler’s formula, a polynomial of ρz is derived to approximate the function relationship between ρx and ρz. If a discrete variable is involved, the marginal transformation is decomposed into piecewise continuous ones, and ρx is expressed as a polynomial of ρz by Taylor expansion. For a given ρx, ρz can be efficiently determined by solving a polynomial equation.  相似文献   

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