共查询到20条相似文献,搜索用时 62 毫秒
1.
Let π1,…,πp be p independent normal populations with means μ1…, μp and variances σ21,…, σ2p respectively. Let X(ni) be a simple random sample of size ni from πi, i = 1,…,p. Given the simple random samples X(n1),…, X(np) from π1,…,πp respectively, a test has been proposed for testing the homogeneity of variances H0: σ21=…σ2p, against the restricted alternative, H1: σ21≥…≥σ2p, with at least one strict inequality. Some properties of the test are discussed and critical values are tabulated. 相似文献
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Kai F. Yu 《统计学通讯:理论与方法》2013,42(7):1745-1753
Let X1,X2,… be independent and identically distributed nonnegative random variables with mean μ, and let Sn = X1 + … + Xn. For each λ > 0 and each n ≥ 1, let An be the interval [λnY, ∞), where γ > 1 is a constant. The number of times that Sn is in An is denoted by N. As λ tends to zero, the asymtotic behavior of N is studied. Specifically under suitable conditions, the expectation of N is shown to be (μλ?1)β + o(λ?β/2 where β = 1/(γ-1) and the variance of N is shown to be (μλ?1)β(βμ1)2σ2 + o(λ?β) where σ2 is the variance of Xn. 相似文献
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Consider an ergodic Markov chain X(t) in continuous time with an infinitesimal matrix Q = (qij) defined on a finite state space {0, 1,…, N}. In this note, we prove that if X(t) is skip-free positive (negative, respectively), i.e., qij, = 0 for j > i+ 1 (i > j+ 1), then the transition probability pij(t) = Pr[X(t)=j | X(0) =i] can be represented as a linear combination of p0N(t) (p(m)(N0)(t)), 0 ≤ m ≤N, where f(m)(t) denotes the mth derivative of a function f(t) with f(0)(t) =f(t). If X(t) is a birth-death process, then pij(t) is represented as a linear combination of p0N(m)(t), 0 ≤m≤N - |i-j|. 相似文献
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《统计学通讯:理论与方法》2013,42(7):1555-1569
ABSTRACT Consider k(≥ 2) independent exponential populations Π1, Π2, …, Π k , having the common unknown location parameter μ ∈ (?∞, ∞) (also called the guarantee time) and unknown scale parameters σ1, σ2, …σ k , respectively (also called the remaining mean lifetimes after the completion of guarantee times), σ i > 0, i = 1, 2, …, k. Assume that the correct ordering between σ1, σ2, …, σ k is not known apriori and let σ[i], i = 1, 2, …, k, denote the ith smallest of σ j s, so that σ[1] ≤ σ[2] ··· ≤ σ[k]. Then Θ i = μ + σ i is the mean lifetime of Π i , i = 1, 2, …, k. Let Θ[1] ≤ Θ[2] ··· ≤ Θ[k] denote the ranked values of the Θ j s, so that Θ[i] = μ + σ[i], i = 1, 2, …, k, and let Π(i) denote the unknown population associated with the ith smallest mean lifetime Θ[i] = μ + σ[i], i = 1, 2, …, k. Based on independent random samples from the k populations, we propose a selection procedure for the goal of selecting the population having the longest mean lifetime Θ[k] (called the “best” population), under the subset selection formulation. Tables for the implementation of the proposed selection procedure are provided. It is established that the proposed subset selection procedure is monotone for a general k (≥ 2). For k = 2, we consider the loss measured by the size of the selected subset and establish that the proposed subset selection procedure is minimax among selection procedures that satisfy a certain probability requirement (called the P*-condition) for the inclusion of the best population in the selected subset. 相似文献
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Hlne Massam 《Revue canadienne de statistique》1995,23(1):67-84
We define the Wishart distribution on the cone of positive definite matrices and an exponential distribution on the Lorentz cone as exponential dispersion models. We show that these two distributions possess a property of exact decomposition, and we use this property to solve the following problem: given q samples (yil,… yiNj), i = l,…,q, from a N(μi,Σi,) distribution, test H:Σ1 = Σ2 = … = σq. Using the exact decomposition property, the classical test statistic for H, involving q parameters pi = (Ni, - l)/2, i = 1,…,q, is replaced by a sequence of q - l test statistics for the sequence of tests Hi,:σ1 =σ2 = … =σi given that Hi-1 is true, i = 2,…,q. Each one of these test statistics involves two parameters only, p.i-1 = p1 + … + pi-1 and pi. We also use the exact decomposition property to test equality of the “direction parameters” for q sample points from the exponential distribution on the Lorentz cone. We give a table of critical values for the distribution on the three-dimensional Lorentz cone. Tables of critical values in higher dimensions can easily be computed following the same method as in dimension three. 相似文献
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M. Samanta 《Australian & New Zealand Journal of Statistics》1986,28(2):164-172
The probability density function (pdf) of a two parameter exponential distribution is given by f(x; p, s?) =s?-1 exp {-(x - ρ)/s?} for x≥ρ and 0 elsewhere, where 0 < ρ < ∞ and 0 < s?∞. Suppose we have k independent random samples where the ith sample is drawn from the ith population having the pdf f(x; ρi, s?i), 0 < ρi < ∞, 0 < s?i < s?i < and f(x; ρ, s?) is as given above. Let Xi1 < Xi2 <… < Xiri denote the first ri order statistics in a random sample of size ni, drawn from the ith population with pdf f(x; ρi, s?i), i = 1, 2,…, k. In this paper we show that the well known tests of hypotheses about the parameters ρi, s?i, i = 1, 2,…, k based on the above observations are asymptotically optimal in the sense of Bahadur efficiency. Our results are similar to those for normal distributions. 相似文献
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Let X1 X2 … XN be independent normal p-vectors with common mean vector $$ = ($$) and common nonsingular covariance matrix $$ = Diag ($sGi) [(1–p) I + pE] Diag ($sGi), $sGi> 0, i = 1… p, 1>p>=1/p–1. Write rij = sample correlation between the i th and the j th variable i j = 1,… p. It has been proved that for testing the hypothesis H0 : p = 0 against the alternative H1 : p>0 where $$ and $sG1,…, $sGp are unknown, the test which rejects H0 for large value of $$ rij is locally best invariant for every $aL: 0 > $aL > 1 and locally minimax as p $$ 0 in the sense of Giri and Kiefer, 1964, for every $aL: 0 > $aL $$ $aL0 > 1 where$aL0 = Pp=0 $$. 相似文献
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Harry Joe 《统计学通讯:理论与方法》2013,42(11):3677-3685
Theorerms are proved for the maxima and minima of IIRi!/IICj!/T!IIyij ! over r× c contingcncy tables Y=(yij) with row sums R1,…,Rr, column sums C1,…,Cc, and grand total T. These results are imlplemented into the network algorithm of Mehta and Patel (1983) for computing the P-value of Fisher's exact test for unordered r×c contingency tables. The decrease in the amount of computing time can be substantial when the column sums are very different. 相似文献
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A RENEWAL THEOREM IN MULTIDIMENSIONAL TIME 总被引:1,自引:0,他引:1
Let Yl, Y2,… be i.i.d., positive, integer-valued random variables with means, μ. Let the sequences {Yij, j= 1,2,…}, i= 1,…, r be independent copies of {Y1, Y2,…}. For n={n1,…, nr.}, n1≥1, let Sn=S?n1k1=1= 1 …S?nrkr=1 Yik1… Yrkr. We show that S?Nk=1S?∞k1=1…S?∞nr=1 P[[Sn= k] ? [μ-r N logr-1 (N)/(r-1)!] as N →∞. 相似文献
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Christian Genest 《Revue canadienne de statistique》1984,12(2):153-163
In this paper, we consider the problem of combining a number of opinions which have been expressed as probability measures P1, …, Pn, over some space. It is shown that a pooling formula which has the marginalization property of McConway (1981) must be of the form T = Σni=1Wi Pi + (1 - Σni =1Wi)Q, where Q is an arbitrary measure and W1, …, Wn ϵ [—1,1] are weights such that| ΣJ Σ j wj | ≤ 1 for every subset J of {1, …, n}. If, in addition, T is required to preserve the independence of arbitrary events A and B whenever these events are independent under each Pi, then either T = Pi for some 1 ≤ i ≤ n or T = Q, in which case Q takes values in {0, l}. 相似文献
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Franois Perron 《Revue canadienne de statistique》1991,19(1):103-108
Let X = (Xj : j = 1,…, n) be n row vectors of dimension p independently and identically distributed multinomial. For each j, Xj is partitioned as Xj = (Xj1, Xj2, Xj3), where pi is the dimension of Xji with p1 = 1,p1+p2+p3 = p. In addition, consider vectors Yji, i = 1,2j = 1,…,ni that are independent and distributed as X1i. We treat here the problem of testing independence between X11 and X13 knowing that X11 and X12 are uncorrected. A locally best invariant test is proposed for this problem. 相似文献
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Serkan Eryilmaz 《统计学通讯:模拟与计算》2017,46(10):8005-8013
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
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In this paper an exact distributional framework is developed for analysing an IxJxK contingency table. It is shown that for the case of hypotheses H0:Pijk=Pi..P.j./K and H0:Pijk =Pi..P.j.P..k the exact distributional results do not follow as simple extensions of the corresponding results obtained for an I×J table under the hypothesis of independence. From the factorial moment generating functions, expressions for the covariance matrices in terms of the Kronecker products of matrices, are presented. These expressions give indications whether or not Pearson's chi-square statistic should be corrected by the factor (n?1)/n or not. Marginal and conditional distributions are considered briefly and important differences with regard to the resuits for marginal and conditional distributions for an IxJ table are mentioned. 相似文献
18.
Let X= (X1,…, Xk)’ be a k-variate (k ≥ 2) normal random vector with unknown population mean vector μ = (μ1 ,…, μk)’ and covariance matrix Σ of order k and let μ[1] ≤ … ≤ μ[k] be the ordered values of the μ ’ s. No prior knowledge of the pairing of the μ[i] with the Xj. (or μ[i] with the σj 2) is assumed for any i and j (1 ≤ i, j ≤ k). Based on a random sample of N independent vector observations on X, this paper considers both upper and lower (one-sided) and two-sided 100γ% (0 < γ < 1) confidence intervals for μ[k] and μ[1], the largest and the smallest mean, respectively, when Σ is known and when Σ is equal to σ2R with common unknown variance σ2 > 0 and correlation matrix R known, respectively. An optimum two-sided confidence interval via finding the shortest length from this class is also considered. Necessary tables and computer program to actually apply these procedures are provided. 相似文献
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《Journal of statistical planning and inference》1997,64(2):205-229
In this paper we consider Bayesian analysis of the generalized growth curve model when the covariance matrix Σ = σ2C where C = (ϱi − j), σ2 > 0 and −1 < ϱ < 1 are unknown. We consider both parameter estimation and prediction of future values. Results are illustrated with real and simulated data. 相似文献
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John E. Angus 《统计学通讯:模拟与计算》2013,42(10):2197-2202
The classical coupon collector's problem is considered, where each new coupon collected is type i with probability pi , ∑ n i = 1 pi = 1. Suppose coupons are collected in a sequence of independent trials. An expression is developed for the probability that all coupon types i, i ≠ j, have been collected prior to collecting r ? 1 coupons of type j in the sequence of trials. Given two different coupon subsets A, B of {1, 2, …, n}, the foregoing is then generalized to an expression for the probability that s ? 1 copies of A appear in the sequence of trials before r ? 1 copies of B. Some computational considerations are discussed. 相似文献