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221.
In this article, we consider the problem of best linear unbiased estimation and best linear invariant estimation of the common scale parameter of several distributions using spacing of the pooled sample of all observations of individual samples. We derived conditions for the non negativity of the scale estimator obtained by the above methods. Further, we obtained necessary and sufficient conditions for the derived estimators to be constant multiples of the pooled sample range. 相似文献
222.
In this article, we introduce a new distribution-free Shewhart-type control chart that takes into account the location of a single order statistic of the test sample (such as the median) as well as the number of observations in that test sample that lie between the control limits. Exact formulae for the alarm rate, the run length distribution, and the average run length (ARL) are all derived. A key advantage of the chart is that, due to its nonparametric nature, the false alarm rate and in-control run length distribution are the same for all continuous process distributions, and so will be naturally robust. Tables are provided for the implementation of the chart for some typical ARL values and false alarm rates. The empirical study carried out reveals that the new chart is preferable from a robustness point of view in comparison to a classical Shewhart-type chart and also the nonparametric chart of Chakraborti et al. (2004). 相似文献
223.
H. Leon Harter 《统计学通讯:理论与方法》2013,42(9):2609-2649
ABSTRACT Harter (1979) summarized applications of order statistics to multivariate analysis up through 1949. The present paper covers the period 1950–1959. References in the two papers were selected from the first and second volumes, respectively, of the author's chronological annotated bibliography on order statistics [Harter (1978, 1983)]. Tintner (1950a) established formal relations between four special types of multivariate analysis: (1) canonical correlation, (2) principal components, (3) weighted regression, and (4) discriminant analysis, all of which depend on ordered roots of determinantal equations. During the decade 1950–1959, numerous authors contributed to distribution theory and/or computational methods for ordered roots and their applications to multivariate analysis. Test criteria for (i) multivariate analysis of variance, (ii) comparison of variance–covariance matrices, and (iii) multiple independence of groups of variates when the parent population is multivariate normal were usually derived from the likelihood ratio principle until S. N. Roy (1953) formulated the union–intersection principles on which Roy & Bose (1953) based their simultaneous test and confidence procedure. Roy & Bargmann (1958) used an alternative procedure, called the step–down procedure, in deriving a test for problem (iii), and J. Roy (1958) applied the step–down procedure to problem (i) and (ii), Various authors developed and applied distribution theory for several multivariate distributions. Advances were also made on multivariate tolerance regions [Fraser & Wormleighton (1951), Fraser (1951, 1953), Fraser & Guttman (1956), Kemperman (1956), and Somerville (1958)], a criterion for rejection of multivariate outliers [Kudô (1957)], and linear estimators, from censored samples, of parameters of multivariate normal populations [Watterson (1958, 1959)]. Textbooks on multivariate analysis were published by Kendall (1957) and Anderson (1958), as well as a monograph by Roy (1957) and a book of tables by Pillai (1957). 相似文献
224.
N. K. Sajeevkumar 《统计学通讯:理论与方法》2013,42(10):1780-1786
In this article, we consider the problem of best linear unbiased estimation and best linear invariant estimation of the scale parameter of a symmetric distribution using quasi-ranges is considered. We also prove a sufficient condition for the non negativity of the scale estimator obtained by the above method. Further, we obtain necessary and sufficient conditions for the derived estimators to be constant multiple of the sample range. 相似文献
225.
Consider k independent random samples with different sample sizes such that the ith sample comes from the cumulative distribution function (cdf) F i = 1 ? (1 ? F)α i , where α i is a known positive constant and F is an absolutely continuous cdf. Also, suppose that we have observed the maximum and minimum of the first k samples. This article shows how one can construct the nonparametric prediction intervals for the order statistics of the future samples on the basis of these information. Three schemes are studied and in each case exact expressions for the prediction coefficients of prediction intervals are derived. Numerical computations are given for illustrating the results. Also, a comparison study is done while the complete samples are available. 相似文献
226.
Xiaomi Hu 《统计学通讯:理论与方法》2013,42(5):1501-1507
AbstractFor several normal mean vectors restricted by a simple ordering with respect to a multivariate order, this article derives sufficient and necessary conditions for the restricted MLEs for both mean vectors and covariance matrix, and develops an ad hoc test. It establishes conditions for the bounds of the p-values. One example of such bound is given with some comments. 相似文献
227.
Serkan Eryilmaz 《统计学通讯:理论与方法》2013,42(19):5628-5636
ABSTRACTLet (Xi, Yi), i = 1, …, n be a pair where the first coordinate Xi represents the lifetime of a component, and the second coordinate Yi denotes the utility of the component during its lifetime. Then the random variable Y[r: n] which is known to be the concomitant of the rth order statistic defines the utility of the component which has the rth smallest lifetime. In this paper, we present a dynamic analysis for an n component system under the above-mentioned concomitant setup. 相似文献
228.
AbstractWe introduce here the truncated version of the unified skew-normal (SUN) distributions. By considering a special truncations for both univariate and multivariate cases, we derive the joint distribution of consecutive order statistics X(r, ..., r + k) = (X(r), ..., X(r + K))T from an exchangeable n-dimensional normal random vector X. Further we show that the conditional distributions of X(r + j, ..., r + k) given X(r, ..., r + j ? 1), X(r, ..., r + k) given (X(r) > t)?and X(r, ..., r + k) given (X(r + k) < t) are special types of singular SUN distributions. We use these results to determine some measures in the reliability theory such as the mean past life (MPL) function and mean residual life (MRL) function. 相似文献
229.
230.
In an earlier paper the authors (1997) extended the results of Hayter (1990) to the two parameter exponential probability model. This paper addressee the extention to the scale parameter case under location-scale probability model. Consider k (k≧3) treatments or competing firms such that an observation from with treatment or firm follows a distribution with cumulative distribution function (cdf) Fi(x)=F[(x-μi)/Qi], where F(·) is any absolutely continuous cdf, i=1,…,k. We propose a test to test the null hypothesis H0:θ1=…=θk against the simple ordered alternative H1:θ1≦…≦θk, with at least one strict inequality, using the data Xi,j, i=1,…k; j=1,…,n1. Two methods to compute the critical points of the proposed test have been demonstrated by talking k two parameter exponential distributions. The test procedure also allows us to construct simultaneous one sided confidence intervals (SOCIs) for the ordered pairwise ratios θj/θi, 1≦i<j≦k. Statistical simulation revealed that: 9i) actual sizes of the critical points are almost conservative and (ii) power of the proposed test relative to some existing tests is higher. 相似文献