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41.
《Journal of Statistical Computation and Simulation》2012,82(8):985-999
Comparisons of best linear unbiased estimators with some other prominent estimators have been carried out over the last 50 years since the ground breaking work of Lloyd [E.H. Lloyd, Least squares estimation of location and scale parameters using order statistics, Biometrika 39 (1952), pp. 88–95]. These comparisons have been made under many different criteria across different parametric families of distributions. A noteworthy one is by Nagaraja [H.N. Nagaraja, Comparison of estimators and predictors from two-parameter exponential distribution, Sankhyā Ser. B 48 (1986), pp. 10–18], who made a comparison of best linear unbiased (BLUE) and best linear invariant (BLIE) estimators in the case of exponential distribution. In this paper, continuing along the same lines by assuming a Type II right censored sample from a scaled-exponential distribution, we first compare BLUE and BLIE of the exponential mean parameter in terms of Pitman closeness (nearness) criterion. We show that the BLUE is always Pitman closer than the BLIE. Next, we introduce the notions of Pitman monotonicity and Pitman consistency, and then establish that both BLUE and BLIE possess these two properties. 相似文献
42.
We introduce the problem of estimation of the parameters of a dynamically selected population in an infinite sequence of random variables and provide its application in the statistical inference based on record values from a non stationary scheme. We develop unbiased estimation of the parameters of the dynamically selected population and evaluate the risk of the estimators. We provide comparisons with natural estimators and obtain asymptotic results. Finally, we illustrate the applicability of the results using real data. 相似文献
43.
Let T2 i=z′iS?1zi, i==,…k be correlated Hotelling's T2 statistics under normality. where z=(z′i,…,z′k)′ and nS are independently distributed as Nkp((O,ρ?∑) and Wishart distribution Wp(∑, n), respectively. The purpose of this paper is to study the distribution function F(x1,…,xk) of (T2 i,…,T2 k) when n is large. First we derive an asymptotic expansion of the characteristic function of (T2 i,…,T2 k) up to the order n?2. Next we give asymptotic expansions for (T2 i,…,T2 k) in two cases (i)ρ=Ik and (ii) k=2 by inverting the expanded characteristic function up to the orders n?2 and n?1, respectively. Our results can be applied to the distribution function of max (T2 i,…,T2 k) as a special case. 相似文献
44.
This paper establishes a nonparametric estimator for the treatment effect on censored bivariate data under unvariate censoring. This proposed estimator is based on the one from Lin and Ying(1993)'s nonparametric bivariate survival function estimator, which is itself a generalized version of Park and Park(1995)' quantile estimator. A Bahadur type representation of quantile functions were obtained from the marginal survival distribution estimator of Lin and Ying' model. The asymptotic property of this estimator is shown below and the simulation studies are also given 相似文献
45.
《统计学通讯:模拟与计算》2013,42(4):619-640
ABSTRACT Area statistics are sample versions of areas occurring in a probability plot of two distribution functions F and G. This paper presents a unified basis for five statistics of this type. They can be used for various testing problems in the framework of the two sample problem for independent observations, such as testing equality of distributions against inequality or testing stochastic dominance of distributions in one or either direction against nondominance. Though three of the statistics considered have already been suggested in literature, two of them are new and deserve our interest. The finite sample distributions of the statistics (under F=G) can be calculated via recursion formulae. Two tables with critical values of the new statistics are included. The asymptotic distribution of the properly normalized versions of the area statistics are functionals of the Brownian bridge. The distribution functions and quantiles thereof are obtained by Monte Carlo simulation. Finally, the power functions of the two new tests based on area statistics are compared to the power functions of the tests based on the corresponding supremum statistics, i.e., statistics of the Kolmogorov–Smirnov type. 相似文献
46.
K. Jayakumar 《统计学通讯:模拟与计算》2013,42(10):3092-3117
AbstractWe introduce a new family of distributions using truncated discrete Linnik distribution. This family is a rich family of distributions which includes many important families of distributions such as Marshall–Olkin family of distributions, family of distributions generated through truncated negative binomial distribution, family of distributions generated through truncated discrete Mittag–Leffler distribution etc. Some properties of the new family of distributions are derived. A particular case of the family, a five parameter generalization of Weibull distribution, namely discrete Linnik Weibull distribution is given special attention. This distribution is a generalization of many distributions, such as extended exponentiated Weibull, exponentiated Weibull, Weibull truncated negative binomial, generalized exponential truncated negative binomial, Marshall-Olkin extended Weibull, Marshall–Olkin generalized exponential, exponential truncated negative binomial, Marshall–Olkin exponential and generalized exponential. The shape properties, moments, median, distribution of order statistics, stochastic ordering and stress–strength properties of the new generalized Weibull distribution are derived. The unknown parameters of the distribution are estimated using maximum likelihood method. The discrete Linnik Weibull distribution is fitted to a survival time data set and it is shown that the distribution is more appropriate than other competitive models. 相似文献
47.
This paper considers the maximum and minimum of a pair of log-normal variables with equal mean. It shows that either order statistic has a smaller coefficient of variation than the two original log-normal variables provided the latter are of equal variance. When the variances are unequal, as the variance ratio increases, the minimum (maximum), has a smaller coefficient of variation if the correlation coefficient of the log-normal variables is small (small) and the variances are large (small). 相似文献
48.
《统计学通讯:理论与方法》2013,42(8):1743-1754
ABSTRACT The display of the data by means of contingency tables is used in different approaches to statistical inference, for example, to broach the test of homogeneity of independent multinomial distributions. We develop a Bayesian procedure to test simple null hypotheses versus bilateral alternatives in contingency tables. Given independent samples of two binomial distributions and taking a mixed prior distribution, we calculate the posterior probability that the proportion of successes in the first population is the same as in the second. This posterior probability is compared with the p-value of the classical method, obtaining a reconciliation between both results, classical and Bayesian. The obtained results are generalized for r × s tables. 相似文献
49.
《统计学通讯:模拟与计算》2013,42(4):949-962
Hill's estimator is a popular method for estimating the thickness of heavy tails. In this paper we modify Hill's estimator to make it shift-invariant as well as scale-invariant. The resulting shifted Hill's estimator is a more robust method of estimating tail thickness. 相似文献
50.
张超 《北京科技大学学报(社会科学版)》2016,32(2):86-93
初唐诏敕文是初唐时期皇帝于施政过程中发布的“王言政令”,是具有最高权威的下行政治公文,涉及到了当时的政治、经济、军事、律法、外交、教育、文化等多方面的史实,和《大唐创业起居注》、《唐太宗实录》等史籍一道,都属于第一手资料,史料价值很高,可补正史之阙。即便是那些旨在宣扬皇德的诏敕文,如皇帝的即位、改元、祭天、封禅诏书,也为我们考察当时的史实提供了很多有价值的线索。本文主要从文史结合的角度出发,通过考察唐武德九年六月至九月诏书,来挖掘其中隐藏的李世民弑兄夺权及李渊被迫让位的真相。 相似文献