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911.
Order statistics from trivariate normal and -distributions in terms of generalized skew-normal and skew- distributions 总被引:1,自引:0,他引:1
We consider here a generalization of the skew-normal distribution, GSN(λ1,λ2,ρ), defined through a standard bivariate normal distribution with correlation ρ, which is a special case of the unified multivariate skew-normal distribution studied recently by Arellano-Valle and Azzalini [2006. On the unification of families of skew-normal distributions. Scand. J. Statist. 33, 561–574]. We then present some simple and useful properties of this distribution and also derive its moment generating function in an explicit form. Next, we show that distributions of order statistics from the trivariate normal distribution are mixtures of these generalized skew-normal distributions; thence, using the established properties of the generalized skew-normal distribution, we derive the moment generating functions of order statistics, and also present expressions for means and variances of these order statistics.Next, we introduce a generalized skew-tν distribution, which is a special case of the unified multivariate skew-elliptical distribution presented by Arellano-Valle and Azzalini [2006. On the unification of families of skew-normal distributions. Scand. J. Statist. 33, 561–574] and is in fact a three-parameter generalization of Azzalini and Capitanio's [2003. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. J. Roy. Statist. Soc. Ser. B 65, 367–389] univariate skew-tν form. We then use the relationship between the generalized skew-normal and skew-tν distributions to discuss some properties of generalized skew-tν as well as distributions of order statistics from bivariate and trivariate tν distributions. We show that these distributions of order statistics are indeed mixtures of generalized skew-tν distributions, and then use this property to derive explicit expressions for means and variances of these order statistics. 相似文献
912.
Rosa Arboretti Giancristofaro Stefano Bonnini Fortunato Pesarin 《Statistics and Computing》2009,19(2):209-216
In many sciences researchers often meet the problem of establishing if the distribution of a categorical variable is more
concentrated, or less heterogeneous, in population P
1 than in population P
2. An approximate nonparametric solution to this problem is discussed within the permutation context. Such a solution has similarities
to that of testing for stochastic dominance, that is, of testing under order restrictions, for ordered categorical variables.
Main properties of given solution and a Monte Carlo simulation in order to evaluate its degree of approximation and its power
behaviour are examined. Two application examples are also discussed. 相似文献
913.
914.
Estimation of a relative potency of two preparations in so-called parallel-line assays is presented. A special type of incomplete
Latin square designs where doses of preparations are administered is considered. Testing hypotheses about similarity of preparations
and their relative potency in the case of correlated observations are regarded. Confidence interval for the relative potency
of preparations is also given. Theoretical considerations are applied to point and interval estimation of potencies of new
tuberculins with respect to some international standards tested in experiments on guinea-pigs. 相似文献
915.
Modified inference about the mean of the exponential distribution using moving extreme ranked set sampling 总被引:1,自引:1,他引:0
The maximum likelihood estimator (MLE) and the likelihood ratio test (LRT) will be considered for making inference about the
scale parameter of the exponential distribution in case of moving extreme ranked set sampling (MERSS). The MLE and LRT can
not be written in closed form. Therefore, a modification of the MLE using the technique suggested by Maharota and Nanda (Biometrika
61:601–606, 1974) will be considered and this modified estimator will be used to modify the LRT to get a test in closed form
for testing a simple hypothesis against one sided alternatives. The same idea will be used to modify the most powerful test
(MPT) for testing a simple hypothesis versus a simple hypothesis to get a test in closed form for testing a simple hypothesis
against one sided alternatives. Then it appears that the modified estimator is a good competitor of the MLE and the modified
tests are good competitors of the LRT using MERSS and simple random sampling (SRS). 相似文献
916.
This paper is concerned with semiparametric discrete kernel estimators when the unknown count distribution can be considered to have a general weighted Poisson form. The estimator is constructed by multiplying the Poisson estimate with a nonparametric discrete kernel-type estimate of the Poisson weight function. Comparisons are then carried out with the ordinary discrete kernel probability mass function estimators. The Poisson weight function is thus a local multiplicative correction factor, and is considered as the uniform measure to detect departures from the equidispersed Poisson distribution. In this way, the effects of dispersion and zero-proportion with respect to the standard Poisson distribution are also minimized. This method of estimation is also applied to the weighted binomial form for the count distribution having a finite support. The proposed estimators, in addition to being simple, easy-to-implement and effective, also outperform the competing nonparametric and parametric estimators in finite-sample situations. Two examples illustrate this new semiparametric estimation. 相似文献
917.
In this article, we introduce three new distribution-free Shewhart-type control charts that exploit run and Wilcoxon-type rank-sum statistics to detect possible shifts of a monitored process. Exact formulae for the alarm rate, the run length distribution, and the average run length (ARL) are all derived. A key advantage of these charts is that, due to their nonparametric nature, the false alarm rate (FAR) and in-control run length distribution is the same for all continuous process distributions. Tables are provided for the implementation of the charts for some typical FAR values. Furthermore, a numerical study carried out reveals that the new charts are quite flexible and efficient in detecting shifts to Lehmann-type out-of-control situations. 相似文献
918.
In this paper, we study the MDPDE (minimizing a density power divergence estimator), proposed by Basu et al. (Biometrika 85:549–559,
1998), for mixing distributions whose component densities are members of some known parametric family. As with the ordinary
MDPDE, we also consider a penalized version of the estimator, and show that they are consistent in the sense of weak convergence.
A simulation result is provided to illustrate the robustness. Finally, we apply the penalized method to analyzing the red
blood cell SLC data presented in Roeder (J Am Stat Assoc 89:487–495, 1994).
This research was supported (in part) by KOSEF through Statistical Research Center for Complex Systems at Seoul National University. 相似文献
919.
In this note we consider the equality of the ordinary least squares estimator (OLSE) and the best linear unbiased estimator
(BLUE) of the estimable parametric function in the general Gauss–Markov model. Especially we consider the structures of the
covariance matrix V for which the OLSE equals the BLUE. Our results are based on the properties of a particular reparametrized version of the
original Gauss–Markov model.
相似文献
920.
Randomized response techniques are widely employed in surveys dealing with sensitive questions to ensure interviewee anonymity
and reduce nonrespondents rates and biased responses. Since Warner’s (J Am Stat Assoc 60:63–69, 1965) pioneering work, many
ingenious devices have been suggested to increase respondent’s privacy protection and to better estimate the proportion of
people, π
A
, bearing a sensitive attribute. In spite of the massive use of auxiliary information in the estimation of non-sensitive parameters,
very few attempts have been made to improve randomization strategy performance when auxiliary variables are available. Moving
from Zaizai’s (Model Assist Stat Appl 1:125–130, 2006) recent work, in this paper we provide a class of estimators for π
A
, for a generic randomization scheme, when the mean of a supplementary non-sensitive variable is known. The minimum attainable
variance bound of the class is obtained and the best estimator is also identified. We prove that the best estimator acts as
a regression-type estimator which is at least as efficient as the corresponding estimator evaluated without allowing for the
auxiliary variable. The general results are then applied to Warner and Simmons’ model. 相似文献