排序方式: 共有17条查询结果,搜索用时 15 毫秒
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Motivated by an application in change point analysis, we derive a closed form for the density function of the sum of n independent, non-identically distributed, uniform random variables. 相似文献
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This paper considers estimation of the parameter of a Poisson distribution using Varian's (1975) asymmetric LINEX loss function L (δ) = b{exp(aδ) - aδ - 1}, where δ is the estimation error and b > 0, a 0. It is shown that for a < 0, the sample mean X¯ is admissible whereas for a > 0, X¯ is dominated by c*X¯, where c*= (n/a)log(1+a/n). Practical implications of this result are indicated. More general results, concerning the admissibility of estimators of the form cX¯+ d are also presented. 相似文献
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For a two-way ANOVA table, with a single observation per cell, the standard approach is to assume that interaction between the two factors is negligible, and to base inferences about the main factors on the model without interaction. But there is no totally satisfactory method for testing if interaction can be ignored. The classical approach is to specify a functional form for the interaction terms, involving a small number of parameters, and then use an appropriate test. But, such tests have low power if the functional form is inappropriate. This has led researchers to propose tests which do not assume a specific form for the interactions. In this article, we present a new approach for testing interaction which also does not assume a specific form for the interaction. This approach is fairly simple and flexible, and its usefulness is illustrated with several examples. We also present a general result which shows that there is no test of interaction with good power properties against all types of interaction. 相似文献
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AbstractThe problem of testing Rayleigh distribution against exponentiality, based on a random sample of observations is considered. This problem arises in survival analysis, when testing a linearly increasing hazard function against a constant hazard function. It is shown that for this problem the most powerful invariant test is equivalent to the “ratio of maximized likelihoods” (RML) test. However, since the two families are separate, the RML test statistic does not have the usual asymptotic chi-square distribution. Normal and saddlepoint approximations to the distribution of the RML test statistic are derived. Simulations show that saddlepoint approximation is more accurate than the normal approximation, especially for tail probabilities that are the main values of interest in hypothesis testing. 相似文献
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In stratified random sampling, it is generally recognised that nonproportional allocation is worthwhile only if the gain in precision is substantial. This note presents a sharp lower bound for the relative precision of proportional to optimum (Neyman) allocation, in terms of the ratio of the largest to the smallest stratum standard deviations. This provides a quick measure of the efficiency of proportional allocation, and may be used as a formal basis for deriving useful practical rules. In particular, it is formally confirmed that for estimating a proportion nonproportional allocation is rarely worthwhile. 相似文献
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This article considers the two-piece normal-Laplace (TPNL) distribution, a split skew distribution consisting of a normal part, and a Laplace part. The distribution is indexed by three parameters, representing location, scale, and shape. As illustrated with several examples, the TPNL family of distributions provides a useful alternative to other families of asymmetric distributions on the real line. However, because the likelihood function is not well behaved, standard theory of maximum-likelihood (ML) estimation does not apply to the TPNL family. In particular, the likelihood function can have multiple local maxima. We provide a procedure for computing ML estimators, and prove consistency and asymptotic normality of ML estimators, using non standard methods. 相似文献
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We derive best-possible bounds on the class of copulas with known values at several points, under the assumption that the points are either in “increasing order” or in “decreasing order”. These bounds may be used to establish best-possible bounds on Kendall's τ and Spearman's ρ, for such copulas. An important special case is when the values of a copula are known at several diagonal points. We also use our results to establish best-possible bounds on the distribution function of the sum of two random variables with known marginal distributions when the values of the joint distribution function are known at several points. 相似文献
9.
For testing separate families of hypotheses, the likelihood ratio test does not have the usual asymptotic properties. This paper considers the asymptotic distribution of the ratio of maximized likelihoods (RML) statistic in the special case of testing separate scale or location-scale families of distributions. We derive saddlepoint approximations to the density and tail probabilities of the log of the RML statistic. These approximations are based on the expansion of the log of the RML statistic up to the second order, which is shown not to depend on the location and scale parameters. The resulting approximations are applied in several cases, including normal versus Laplace, normal versus Cauchy, and Weibull versus log-normal. Our results show that the saddlepoint approximations are satisfactory, even for fairly small sample sizes, and are more accurate than normal approximations and Edgeworth approximations, especially for tail probabilities that are the values of main interest in hypothesis testing problems. 相似文献
10.
We consider the problem of testing normality against the logistic distribution, based on a random sample of observations. Since the two families are separate (non nested), the ratio of maximized likelihoods (RML) statistic does not have the usual asymptotic chi-square distribution. We derive the saddlepoint approximation to the distribution of the RML statistic and show that this approximation is more accurate than the normal and Edgeworth approximations, especially for tail probabilities that are the main values of interest in hypothesis testing. It is also shown that this test is almost identical to the most powerful invariant test. 相似文献