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2.
The lifetime of an ordinary k-out-of-n system is described by the (n–k+1)-st order statistic from an iid sample. This set-up is based on the assumption that the failure of any component does not affect the remaining ones. Since this is possibly not fulfilled in technical systems, sequential order statistics have been proposed to model a change of the residual lifetime distribution after the breakdown of some component. We investigate such sequential k-out-of-n systems where the corresponding sequential order statistics, which describe the lifetimes of these systems, are based on one- and two-parameter exponential distributions. Given differently structured systems, we focus on three estimation concepts for the distribution parameters. MLEs, UMVUEs and BLUEs of the location and scale parameters are presented. Several properties of these estimators, such as distributions and consistency, are established. Moreover, we illustrate how two sequential k-out-of-n systems based on exponential distributions can be compared by means of the probability P(X < Y). Since other models of ordered random variables, such as ordinary order statistics, record values and progressive type II censored order statistics can be viewed as sequential order statistics, all the results can be applied to these situations as well. 相似文献
3.
T. Ramallingam 《Annals of the Institute of Statistical Mathematics》1989,41(4):677-681
The exact probability density function of linear combinations of k=k(n) order statistics selected from the whole order statistics (L-statistic) based on a random sample of size n from the uniform distribution on [0, 1] was derived by Matsunawa (1985, Ann. Inst. Statist. Math., 37, 1–16). As the main expression for the density function given by Matsunawa is not complete for the general situation, we first provide the corrections for this formula. Second, we propose a simple scheme involving symbolic computing for evaluating the corrected version of the density function. The cumulative distribution function and the r-th mean of his L-statistic are also derived. 相似文献
4.
P. A. Scarf 《商业与工业应用随机模型》1993,9(3):267-278
The connection between extreme values and record-low values is exploited to derive simply the limiting joint distribution of the r largest order statistics. The use of this distribution in the modelling of corrosion phenomena is considered, and the extrapolation of maxima in space and time is described in this context. There has been recent emphasis on movement away from classical extreme value theory to more efficient estimation procedures. This shift is continued with the illustration of the extra precision of predicted maxima obtained from a model based on extreme order statistics over the classical extreme value approach. 相似文献
5.
Rita Aggarwala N. Balakrishnan 《Annals of the Institute of Statistical Mathematics》1996,48(4):757-771
In this paper, we establish several recurrence relations satisfied by the single and product moments of progressive Type-II right censored order statistics from an exponential distribution. These relations may then be used, for example, to compute all the means, variances and covariances of exponential progressive Type-II right censored order statistics for all sample sizes n and all censoring schemes (R
1, R
2, ..., R
m
), mn. The results presented in the paper generalize the results given by Joshi (1978, Sankhy Ser. B, 39, 362–371; 1982, J. Statist. Plann. Inference, 6, 13–16) for the single moments and product moments of order statistics from the exponential distribution.To further generalize these results, we consider also the right truncated exponential distribution. Recurrence relations for the single and product moments are established for progressive Type-II right censored order statistics from the right truncated exponential distribution. 相似文献
6.
We show that the principal order ideal of an element w in the Bruhat order on involutions in a symmetric group is a Boolean lattice if and only if w avoids the patterns 4321, 45312 and 456123. Similar criteria for signed permutations are also stated. Involutions with this
property are enumerated with respect to natural statistics. In this context, a bijective correspondence with certain Motzkin
paths is demonstrated.
This article is largely based on results from the second author’s M.Sc. thesis [15]. 相似文献
7.
In the nonlinear regression model we consider the optimal design problem with a second order design D-criterion. Our purpose is to present a general approach to this problem, which includes the asymptotic second order bias and variance criterion of the least squares estimator and criteria using the volume of confidence regions based on different statistics. Under assumptions of regularity for these statistics a second order approximation of the volume of these regions is derived which is proposed as a quadratic optimality criterion. These criteria include volumes of confidence regions based on the u
n
- representable statistics. An important difference between the criteria presented in this paper and the second order criteria commonly employed in the recent literature is that the former criteria are independent of the vector of residuals. Moreover, a refined version of the commonly applied criteria is obtained, which also includes effects of nonlinearity caused by third derivatives of the response function. 相似文献
8.
G. S. Lingappaiah 《Annals of the Institute of Statistical Mathematics》1985,37(1):151-163
Summary This paper analyses the shift in parameter of a life test model. This analysis depends on the prediction of order statistics
in future samples based on order statistics in a series of earlier samples in life tests having a general exponential model.
While a series ofk samples are being drawn, model itself undergoes a change. Firstly, a single shift is considered and the effect of this shift
on the variance is discussed. Generalisation withs shifts (s≦k) ink samples in also taken up and the semi-or-used priors (SOUPS) have been used to get predictive distributions. Finally, shift
afteri (i≦k) stages, from exponential to gamma model is considered and for this case effect of the shift on the variance as well as on
the Bayesian prediction region (BPR) is analysed along with set of tables. 相似文献
9.
Donald Lien 《Extremes》2005,8(1-2):79-83
Assume that (X,Y) is a bivariate lognormal vector. Let u = ln(X) and v = ln(Y). Then (u, v) is normally distributed. This note examines the effects of the distribution parameters of (u, v) on the first two moments of the order statistics of (X,Y).
AMS 2000 Subject Classification Primary—62G30 相似文献
10.
T. Matsunawa 《Annals of the Institute of Statistical Mathematics》1985,37(1):1-16
Summary The exact probability density function is given for linear combinations ofk=k(n) order statistics selected from whole order statistics based on random sample of sizen drawn from a uniform distribution. Normal approximation to the linear combinations is made with the aid of Berry-Esseen's
theorem. Necessary and sufficient conditions of the asymptotic normality for the statistic are obtained, too. An exact distribution
and its normal approximation of linear combination of mutually independent gamma variables with integer valued parameters
are also given as associated consequences.
The Institute of Statistical Mathematics 相似文献
11.
k-out-of-n systems frequently appear in applications. They consist of n components of the same kind with independent and identically distributed life-lengths. The life-length of such a system is described by the (n–k+1)-th order statistic in a sample of size n when assuming that remaining components are not affected by failures. Sequential order statistics are introduced as a more flexible model to describe sequential k-out-of-n systems in which the failure of any component possibly influences the other components such that their underlying failure rate is parametrically adjusted with respect to the number of preceding failures. Useful properties of the maximum likelihood estimators of the model parameters are shown, and several tests are proposed to decide whether the new model is the more appropriate one in a given situation. Moreover, for specific distributions, e.g. Weibull distributions, simultaneous maximum likelihood estimation of the model parameters and distribution parameters is considered. 相似文献
12.
Approximation to the expectation of a function of order statistics and its applications 总被引:4,自引:0,他引:4
程士宏 《应用数学学报(英文版)》1997,13(1):71-86
ThisprojectissupportedbytheNationalNaturalScienceFoundationofChinaandDoctoralProgramFoundationofHigherEducation.1.IntroductionLetUI,U2,'bei.i.d.randomvariableswithuniformd.f.ontheinterval(0,l),andforeveryn31,writeUt,,15'5Un,.fortheorderstatisticsofUI,'tUn.SupposethatXI1X2,'arei.i.d.observationsfromanondegenerated.f.F,anddenotebyX.,l5'5X.,.theorderstatisticsofXI,'IX,,'Withoutlossofgenerality,wewillassume0相似文献
13.
We introduce a class of asymptotically unbiased estimators for the second order parameter in extreme value statistics. The estimators are constructed by means of an appropriately chosen linear combination of two simple, but biased, kernel estimators for the second order parameter. Asymptotic normality is proven under a third order condition on the tail behavior, some conditions on the kernel functions and for an intermediate number of upper order statistics. A specific member from the proposed class, obtained with power kernel functions, is derived and its finite sample behavior studied in a small simulation experiment. 相似文献
14.
SOME COMPARISONS BETWEEN GENERALIZED ORDER STATISTICS 总被引:1,自引:0,他引:1
Qiu Guoxin Wang Jinshan 《高校应用数学学报(英文版)》2007,22(3):325-333
Some stochastic comparisons of generalized order statistics under the right spread order,the location independent riskier order and the total time transform order are investigated in this paper.The underlying distributions and parameters on which generalized order statistics are based are also surveyed to obtain the conditions for increasing the expectations of spacings between the first two generalized order statistics and between the last two generalized order statistics. 相似文献
15.
Let R be a commutative ring, let G be a finite group acting on R as automorphisms of R and let R * G be the skew group ring. By using the decomposition subgroups of G, the inertial subgroups of G, the properties of the coefficient ring R and the properties of the fixed subring R
G
, some necessary and sufficient conditions for R * G to be a prime Goldie ring, a semi-hereditary order in a simple Artinian ring, or a Prüfer order in a simple Artinian ring are given. 相似文献
16.
Fork 0 fixed we consider the joint distribution functionF
n
k
of then-k smallest order statistics ofn real-valued independent, identically distributed random variables with arbitrary cumulative distribution functionF. The main result of the paper is a complete characterization of the limit behaviour ofF
n
k
(x
1,,x
n-k) in terms of the limit behaviour ofn(1-F(x
n)) ifn tends to infinity, i.e., in terms of the limit superior, the limit inferior, and the limit if the latter exists. This characterization can be reformulated equivalently in terms of the limit behaviour of the cumulative distribution function of the (k+1)-th largest order statistic. All these results do not require any further knowledge about the underlying distribution functionF. 相似文献
17.
We define the (n,i,f)-tube orders, which include interval orders, trapezoid orders, triangle orders, weak orders, order dimension n, and interval-order-dimension n as special cases. We investigate some basic properties of (n,i,f)-tube orders, and begin classifying them by containment.
Mathematics Subject Classifications (2000) 06A06, 05C62. 相似文献
18.
In this paper, the joint distribution of some special linear combinations of the (internally) studentized order statistics are derived for both normal and exponential populations; the exact relationship between their pdf's is also obtained. The exact sampling distributions of studentized extreme deviation statistic, which has been proposed by Pearson and Chandra Sekar (1936,Biometrika,28, 308–320), are derived for these two populations. An application to the most powerful location and scale invariant test is discussed briefly. 相似文献
19.
Barry C. Arnold 《Journal of multivariate analysis》1985,17(3):316-332
Let X1, X2,…, Xn be identically distributed possibly dependent random variables with finite pth absolute moment assumed without loss of generality to be equal to 1. Denote the order statistics by X1:n, X2:n,…, Xn:n. Bounds are derived for E(Xn:n) when it is assumed that the Xi's are (i) arbitrarily dependent and (ii) independent. The effect of assuming a symmetric common distribution for the Xi's is discussed. Analogous bounds are described for the expected range of the sample. Bounds on expectations of general linear combinations of order statistics are described in the independent case. 相似文献
20.
Kimmo Eriksson 《Journal of Algebraic Combinatorics》1995,4(3):233-252
We explore the connection between polygon posets, which is a class of ranked posets with an edge-labeling which satisfies certain polygon properties, and the weak order of Coxeter groups. We show that every polygon poset is isomorphic to a join ideal in the weak order, and for Coxeter groups where no pair of generators have infinite order the converse is also true.The class of polygon posets is seen to include the class of generalized quotients defined by Björner and Wachs, while itself being included in the class of alternative generalized quotients also considered by these authors. By studying polygon posets we are then able to answer an open question about common properties of these two classes. 相似文献