共查询到20条相似文献,搜索用时 15 毫秒
1.
Michael D. Huffman 《统计学通讯:理论与方法》2013,42(12):3063-3074
Suppose two Poisson processes with rates γ1 and γ2 are observed for fixed times tl and t2. This paper considers hypothesis tests and confidence intervals for the parameter ρ = γ2/γ1. Uniformly most powerful unbiased tests and uniformly most accurate unbiased confidence intervals exist for ρ, but they require randomization and so are not used in practice. Several alternative procedures have been proposed. In the context of one-sided hypothesis tests these procedures are reviewed and compared on numerical grounds and by use of the conditionality and repeated sampling principles. It is argued that a conditional binomial test which rejects with conditional level closest to but not necessarily less than, the nominal a is the most reasonable. This test is different from the usual conditional binomial test which rejects with conditional level closeset to but less than or equal to the nominal α Numerical results indicate that an approximate procedure based on the Poisson variance stabilizing transformation has properties similar to the preferred conditional binomial test. Values for λ1 = t1λ1 required to achieve a specified power are considered. These results are also discussed in terms of test inversion to obtain confidence intervals. 相似文献
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David P.T. Chu 《Revue canadienne de statistique》1993,21(3):285-293
We study the r-content Δ of the r -simplex generated by r+ 1 independent random points in R”. Each random point Zj is isotropic and distributed according to λ||Zj||2 ~ beta-type-2(n/2, v), λ, v > 0. We provide an asymptotic normality result which is analogous to the conjecture made by Miles (1971). A method is introduced to work out the exact density of W = (rλ)r(r!Δ)2/(r + |)r+l and hence that of Δ. The distribution of W is also related to some hypothesis-testing problems in multivariate analysis. Furthermore, by using this method, the distribution of W or Δ can easily be simulated. 相似文献
4.
Let X 1,X 2,…,X n be independent exponential random variables such that X i has hazard rate λ for i = 1,…,p and X j has hazard rate λ* for j = p + 1,…,n, where 1 ≤ p < n. Denote by D i:n (λ, λ*) = X i:n ? X i?1:n the ith spacing of the order statistics X 1:n ≤ X 2:n ≤ ··· ≤ X n:n , i = 1,…,n, where X 0:n ≡ 0. It is shown that the spacings (D 1,n ,D 2,n ,…,D n:n ) are MTP2, strengthening one result of Khaledi and Kochar (2000), and that (D 1:n (λ2, λ*),…,D n:n (λ2, λ*)) ≤ lr (D 1:n (λ1, λ*),…,D n:n (λ1, λ*)) for λ1 ≤ λ* ≤ λ2, where ≤ lr denotes the multivariate likelihood ratio order. A counterexample is also given to show that this comparison result is in general not true for λ* < λ1 < λ2. 相似文献
5.
David D. Hanagal 《统计学通讯:理论与方法》2013,42(5):1273-1295
In this paper, two bivariate exponential distributions based on time(right) censored samples are presented. We assume that the censoring time is independent of the life-times of the two components. This paper obtains comparison of different tests for testing zero and non-zero values of the parameter λ3 which measures the degree of dependence between the two components and also testing symmetry of the two components or λ1=λ2 in the bivariate exponential distribution (BVED) formulated by Marshall and Olkin (1967) based on the above censored sample. It is observed from simulated study that the test based on MLE's performs better in both tests of independence as well as symmetry. The above results have been extended also in Block and Basu (19874) model. 相似文献
6.
Chung-yi Suen 《统计学通讯:理论与方法》2013,42(10):3875-3881
A method of constructing a resolvable orthogonal array (4λk2,2) which can be partitioned into λ orthogonal arrays (4,k 2,1) is proposed. The number of constraints kfor this type of orthogonal array is at most 3λ. When λ=2 or a multiple of 4, an orthogonal array with the maximum number of constraints of 3λ can be constructed. When λ=4n+2(n≧1) an orthogonal array with 2λ+2 constraints can be constructed. When λ is an odd number, orthogonal arrays can be constructed for λ=3,5,7, and 9 with k=4,8,12, and 13 respectively. 相似文献
7.
The generalized lambda distribution, GLD(λ1, λ2 λ3, λ4), is a four-parameter family that has been used for fitting distributions to a wide variety of data sets. The analysis of the λ3 and λ4 values that actually yield valid distributions has (until now) been incomplete. Moreover, because of computational problems and theoretical shortcomings, the moment space over which the GLD can be applied has been limited. This paper completes the analysis of the λ3 and λ4 values that are associated with valid distributions, improves previous computational methods to reduce errors associated with fitting data, expands the parameter space over which the GLD can be used, and uses a four-parameter generalized beta distribution to cover the portion of the parameter space where the GLD is not applicable. In short, the paper extends the GLD to an EGLD system that can be used for fitting distributions to data sets that that are cited in the literature as actually occurring in practice. Examples of use of the proposed system are included 相似文献
8.
Consider the problem of testing the composite null hypothesis that a random sample X1,…,Xn is from a parent which is a member of a particular continuous parametric family of distributions against an alternative that it is from a separate family of distributions. It is shown here that in many cases a uniformly most powerful similar (UMPS) test exists for this problem, and, moreover, that this test is equivalent to a uniformly most powerful invariant (UMPI) test. It is also seen in the method of proof used that the UMPS test statistic Is a function of the statistics U1,…,Un?k obtained by the conditional probability integral transformations (CPIT), and thus that no Information Is lost by these transformations, It is also shown that these optimal tests have power that is a nonotone function of the null hypothesis class of distributions, so that, for example, if one additional parameter for the distribution is assumed known, then the power of the test can not lecrease. It Is shown that the statistics U1, …, Un?k are independent of the complete sufficient statistic, and that these statistics have important invariance properties. Two examples at given. The UMPS tests for testing the two-parameter uniform family against the two-parameter exponential family, and for testing one truncation parameter distribution against another one are derived. 相似文献
9.
Yiying Zhang 《统计学通讯:理论与方法》2017,46(10):5056-5071
In this article, we establish some new results on stochastic comparisons of the maxima of two heterogenous gamma variables with different shape and scale parameters. Let X1 and X2 [X*1 and X*2] be two independent gamma variables with Xi?[X*i] having shape parameter ri?[r*i] and scale parameter λi?[λ*i], i = 1, 2. It is shown that the likelihood ratio order holds between the maxima, X2: 2 and X*2: 2 when λ1 = λ*1 ? λ2 = λ*2 and r1 ? r*1 ? r2 = r*2. We also prove that, if ri, r*i ∈ (0, 1], (r1, r2) majorizes (r*1, r2*), and (λ1, λ2) is p-larger than (λ*1, λ2*), then X2: 2 is larger than X*2: 2 in the sense of the hazard rate order [dispersive order]. Some numerical examples are provided to illustrate the main results. The new results established here strengthen and generalize some of the results known in the literature. 相似文献
10.
Shiue and Bain proposed an approximate F statistic for testing equality of two gamma distribution scale parameters in presence of a common and unknown shape parameter. By generalizing Shiue and Bain's statistic we develop a new statistic for testing equality of L >= 2 gamma distribution scale parameters. We derive the distribution of the new statistic ESP for L = 2 and equal sample size situation. For other situations distribution of ESP is not known and test based on the ESP statistic has to be performed by using simulated critical values. We also derive a C(α) statistic CML and develop a likelihood ratio statistic, LR, two modified likelihood ratio statistics M and MLB and a quadratic statistic Q. The distribution of each of the statistics CML, LR, M, MLB and Q is asymptotically chi-square with L - 1 degrees of freedom. We then conducted a monte-carlo simulation study to compare the perfor- mance of the statistics ESP, LR, M, MLB, CML and Q in terms of size and power. The statistics LR, M, MLB and Q are in general liberal and do not show power advantage over other statistics. The statistic CML, based on its asymptotic chi-square distribution, in general, holds nominal level well. It is most powerful or nearly most powerful in most situations and is simple to use. Hence, we recommend the statistic CML for use in general. For better power the statistic ESP, based on its empirical distribution, is recommended for the special situation for which there is evidence in the data that λ1 < … < λL and n1 < … < nL, where λ1 …, λL are the scale parameters and n1,…, nL are the sample sizes. 相似文献
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The statistical inference drawn from the difference between two independent Poisson parameters is often discussed in the medical literature. However, such discussions are usually based on the frequentist viewpoint rather than the Bayesian viewpoint. Here, we propose an index θ=P(λ1, post<λ2, post), where λ1, post and λ2, post denote Poisson parameters following posterior density. We provide an exact and an approximate expression for calculating θ using the conjugate gamma prior and compare the probabilities obtained using the approximate and the exact expressions. Moreover, we also show a relation between θ and the p-value. We also highlight the significance of θ by applying it to the result of actual clinical trials. Our findings suggest that θ may provide useful information in a clinical trial. 相似文献
12.
Ryszard Zielinski 《Statistics》2013,47(2):223-227
Given λ∈(0-,l), let xλ(F) denote the unique λ-quantile of the distribution F. A distribution-free median-unbiased estimator of xλ(F) is explicitly constructed 相似文献
13.
A single unit system supported by N-l inactive standbys and a repair facility is considered when λ,μ are unknown, λand μbeing failure and repair rates of the unit respectively. Three sampling schemes are considered to obtain moment estimators λ?:and μ ?:when the performance of the unit have to be observed in the system only. Asymptotic variances of the estimates are supplied. 相似文献
14.
M. Ishaq Bhatti 《Statistical Papers》2000,41(3):345-352
Sen Gupta (1988) considered a locally most powerful (LMP) test for testing nonzero values of the equicorrelation coefficient
of a standard symmetric multivariate normal distribution. This paper constructs analogous tests for the symmetric multivariate
normal distribution. It shows that the new test is uniformly most powerful invariant even in the presence of a nuisance parameter,
σ2. Further applications of LMP invariant tests to several equicorrelated populations have been considered and an extension
to panel data modeling has been suggested. 相似文献
15.
Narayan C. Giri 《Revue canadienne de statistique》1988,16(4):419-428
Let X =(x)ij=(111, …, X,)T, i = l, …n, be an n X random matrix having multivariate symmetrical distributions with parameters μ, Σ. The p-variate normal with mean μ and covariance matrix is a member of this family. Let be the squared multiple correlation coefficient between the first and the succeeding p1 components, and let p2 = + be the squared multiple correlation coefficient between the first and the remaining p1 + p2 =p – 1 components of the p-variate normal vector. We shall consider here three testing problems for multivariate symmetrical distributions. They are (A) to test p2 =0 against; (B) to test against =0, 0; (C) to test against p2 =0, We have shown here that for problem (A) the uniformly most powerful invariant (UMPI) and locally minimax test for the multivariate normal is UMPI and is locally minimax as p2 0 for multivariate symmetrical distributions. For problem (B) the UMPI and locally minimax test is UMPI and locally minimax as for multivariate symmetrical distributions. For problem (C) the locally best invariant (LBI) and locally minimax test for the multivariate normal is also LBI and is locally minimax as for multivariate symmetrical distributions. 相似文献
16.
《Journal of statistical planning and inference》1997,59(1):79-100
For series systems with k components it is assumed that the cause of failure is known to belong to one of the 2k − 1 possible subsets of the failure-modes. The theoretical time to failure due to k causes are assumed to have independent Weibull distributions with equal shape parameters. After finding the MLEs and the observed information matrix of (λ1, …, λk, β), a prior distribution is proposed for (λ1, …, λk), which is shown to yield a scale-invariant noninformative prior as well. No particular structure is imposed on the prior of β. Methods to obtain the marginal posterior distributions of the parameters and other parametric functions of interest and their Bayesian point and interval estimates are discussed. The developed techniques are illustrated using a numerical example. 相似文献
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Goodness-of-Fit of the Distribution of Time-to-First-Occurrence in Recurrent Event Models 总被引:1,自引:1,他引:0
Imperfect repair models are a class of stochastic models that deal with recurrent phenomena. This article focuses on the Block, Borges, and Savits (1985) age-dependent minimal repair model (the BBS model) in which a system that fails at time t undergoes one of two types of repair: with probability p(t), a perfect repair is performed, or with probability 1-p(t), a minimal repair is performed. The goodness-of-fit problem of interest concerns the initial distribution of the failure ages. In particular, interest is on testing the null hypothesis that the hazard rate function of the time-to-first-event-occurrence, λ(·), is equal to a prespecified hazard rate function λ0(·). This paper extends the class of hazard-based smooth goodness-of-fit tests introduced in Peña (1998a) to the case where data accrual is from a BBS model. The goodness-of-fit tests are score tests derived by reformulating Neyman's idea of smooth tests in terms of hazard functions. Omnibus as well as directional tests are developed and simulation results are presented to illustrate the sensitivities of the proposed tests for certain types of alternatives. 相似文献
19.
J.Q. Longyear 《Journal of statistical planning and inference》1981,5(2):181-187
A nest with parameters (r,k,λ)→(r′,k′,λ′) is a BIBD on (b,v,r,k,λ) where each block has a distinguished sublock of cardinality k, the sublocks forming a (b,v,r,k,λ)-design.These designs are ‘nested’ in the sense of W.T. Federer (1972), who recommended the use of these designs for the sequential addition of periods in marketing experiments in order to retain Youden design properties as rows are added. Note that for a Youden design, the b columns and v treatments are in an SBIBD arrangement with parameters v=b, k=r, and λ. 相似文献
20.
In this article, a semi-Markovian random walk with delay and a discrete interference of chance (X(t)) is considered. It is assumed that the random variables ζ n , n = 1, 2,…, which describe the discrete interference of chance form an ergodic Markov chain with ergodic distribution which is a gamma distribution with parameters (α, λ). Under this assumption, the asymptotic expansions for the first four moments of the ergodic distribution of the process X(t) are derived, as λ → 0. Moreover, by using the Riemann zeta-function, the coefficients of these asymptotic expansions are expressed by means of numerical characteristics of the summands, when the process considered is a semi-Markovian Gaussian random walk with small drift β. 相似文献