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1.
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
2.
N. Balakrishnan Qihao Xie D. Kundu 《Annals of the Institute of Statistical Mathematics》2009,61(1):251-274
In reliability and life-testing experiments, the researcher is often interested in the effects of extreme or varying stress
factors such as temperature, voltage and load on the lifetimes of experimental units. Step-stress test, which is a special
class of accelerated life-tests, allows the experimenter to increase the stress levels at fixed times during the experiment
in order to obtain information on the parameters of the life distributions more quickly than under normal operating conditions.
In this paper, we consider the simple step-stress model from the exponential distribution when there is time constraint on
the duration of the experiment. We derive the maximum likelihood estimators (MLEs) of the parameters assuming a cumulative
exposure model with lifetimes being exponentially distributed. The exact distributions of the MLEs of parameters are obtained
through the use of conditional moment generating functions. We also derive confidence intervals for the parameters using these
exact distributions, asymptotic distributions of the MLEs and the parametric bootstrap methods, and assess their performance
through a Monte Carlo simulation study. Finally, we present two examples to illustrate all the methods of inference discussed
here. 相似文献
3.
Sofiya Ostrovska 《Numerical Algorithms》2007,44(1):69-82
Since in the case q > 1, q-Bernstein polynomials are not positive linear operators on C[0,1], the study of their approximation properties is essentially more difficult than that for 0<q<1. Despite the intensive research conducted in the area lately, the problem of describing the class of functions in C[0,1] uniformly approximated by their q-Bernstein polynomials (q > 1) remains open. It is known that the approximation occurs for functions admit ting an analytic continuation into a disc
{z:|z| < R}, R > 1. For functions without such an assumption, no general results on approximation are available. In this paper, it is shown
that the function f(x) = ln (x + a), a > 0, is uniformly approximated by its q-Bernstein polynomials (q > 1) on the interval [0,1] if and only if a ≥ 1.
相似文献
4.
We consider a family of Newton-type iterative processes solving nonlinear equations in Banach spaces, that generalizes the
usually iterative methods of R-order at least three. The convergence of this family in Banach spaces is usually studied when the second derivative of the
operator involved is Lipschitz continuous and bounded. In this paper, we relax the first condition, assuming that ‖F″(x)−F″(y)‖≤ω(‖x−y‖), where ω is a nondecreasing continuous real function. We prove that the different R-orders of convergence that we can obtain depend on the quasihomogeneity of the function ω. We end the paper by applying the study to some nonlinear integral equations.
This work was supported by the Ministry of Science and Technology (BFM 2002-00222), the University of La Rioja (API-04/13)
and the Government of La Rioja (ACPI 2003/2004). 相似文献
5.
Let F(x) be a distribution function supported on [0, ∞) with an equilibrium distribution function F
e
(x). In this paper we pay special attention to the hazard rate function r
e
(x) of F
e
(x), which is also called the equilibrium hazard rate (E.H.R.) of F(x). By the asymptotic behavior of r
e
(x) we give a criterion to identify F(x) to be heavy-tailed or light-tailed. Moreover, we introduce two subclasses of heavy-tailed distributions, i.e., ℳ and ℳ*, where ℳ contains almost all the most important heavy-tailed distributions in the literature. Some further discussions on the closure
properties of ℳ and ℳ* under convolution are given, showing that both of them are ideal heavy-tailed subclasses. In the paper we also study the
model of independent difference ξ = Z − θ, where Z and θ are two independent and non-negative random variables. We give intimate relationships of the tail distributions of ξ and Z, as well as relationships of tails of their corresponding equilibrium distributions. As applications, we apply the properties
of class ℳ to risk theory. In the final, some miscellaneous problems and examples are laid, showing the complexity of characterizations
on heavy-tailed distributions by means of r
e
(x).
相似文献
6.
This paper discusses inference for ordered parameters of multinomial distributions. We first show that the asymptotic distributions
of their maximum likelihood estimators (MLEs) are not always normal and the bootstrap distribution estimators of the MLEs
can be inconsistent. Then a class of weighted sum estimators (WSEs) of the ordered parameters is proposed. Properties of the
WSEs are studied, including their asymptotic normality. Based on those results, large sample inferences for smooth functions
of the ordered parameters can be made. Especially, the confidence intervals of the maximum cell probabilities are constructed.
Simulation results indicate that this interval estimation performs much better than the bootstrap approaches in the literature.
Finally, the above results for ordered parameters of multinomial distributions are extended to more general distribution models.
This work was supported by National Natural Science Foundation of China (Grant No. 10371126) 相似文献
7.
The extremal dependence behavior of t copulas is examined and their extreme value limiting copulas, called the t-EV copulas, are derived explicitly using tail dependence functions. As two special cases, the Hüsler–Reiss and the Marshall–Olkin
distributions emerge as limits of the t-EV copula as the degrees of freedom go to infinity and zero respectively. The t copula and its extremal variants attain a wide range in the set of bivariate tail dependence parameters.
Supported by NSERC Discovery Grant. 相似文献
8.
Carsten Trenkler 《Computational Statistics》2008,23(1):19-39
Following Doornik (J Econ Surv 12:573–593, 1998) I present a procedure to approximate the asymptotic distributions of systems
cointegration tests with a prior adjustment for deterministic terms suggested by Lütkepohl (Econometrica 72:647–662, 2004),
Saikkonen and Lütkepohl (Econometric Theory 16:373–406, 2000a, J Business Econ Stat 18:451–464, 2000b, Time Series Anal 21:435–456,
2000c) and Saikkonen and Luukkonen (J Econ 81:93–126, 1997). These tests rely upon different assumptions as to the inclusion
of deterministic components such as a constant, a linear trend or a level shift. The asymptotic distributions, which are functions
of Brownian motions, are approximated by Gamma distributions. Only estimates of the mean and variance of the asymptotic test
distributions are needed to fit the Gamma distributions. Such estimates are obtained from response surfaces. The required
coefficients to compute the asymptotic moments are presented in this paper. Via the fitted Gamma distributions one can, then,
easily derive p-values or arbitrary percentiles. 相似文献
9.
In this article we deal with the problem of stability of the conclusions from principal components analysis over repeated
samples. We define a measure of stability for each component and investigate some of the measures properties. We then obtain
the maximum likelihood estimators (MLEs) of the measures, and derive their joint limiting distributions. The MLEs of the measures
turn out to be asymptotically unbiased and jointly have the multivariate normal distribution. Modified estimators are also
found to reduce the amount of bias in the MLEs. To facilitate interpretation of the measures we define stability confidence
level as coverage probability, and associate with each measure a stability confidence level to describe the measure in terms
of probability. Finally, we investigate the stability of the components via a simulation study and compare the performance
of the MLEs and the modified estimators in terms of bias and precision.
This work was sponsored by a grant from the Office of Vice-President for Research at Kuwait University under project number
SS049. 相似文献
10.
Iterative Approximation of Statistical Distributions and Relation to Information Geometry 总被引:1,自引:0,他引:1
The optimal control of stochastic processes through sensor estimation of probability density functions is given a geometric
setting via information theory and the information metric. Information theory identifies the exponential distribution as the
maximum entropy distribution if only the mean is known and the Γ distribution if also the mean logarithm is known. The surface
representing Γ models has a natural Riemannian information metric. The exponential distributions form a one-dimensional subspace
of the two-dimensional space of all Γ distributions, so we have an isometric embedding of the random model as a subspace of
the Γ models. This geometry provides an appropriate structure on which to represent the dynamics of a process and algorithms
to control it. This short paper presents a comparative study on the parameter estimation performance between the geodesic
equation and the B-spline function approximations when they are used to optimize the parameters of the Γ family distributions. In this case,
the B-spline functions are first used to approximate the Γ probability density function on a fixed length interval; then the coefficients
of the approximation are related, through mean and variance calculations, to the two parameters (i.e. μ and β) in Γ distributions.
A gradient based parameter tuning method has been used to produce the trajectories for (μ, β) when B-spline functions are used, and desired results have been obtained which are comparable to the trajectories obtained from
the geodesic equation.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
11.
Peng Bai 《Journal of multivariate analysis》2007,98(9):1840-1852
This paper studies the exact distributions of the MLEs of the regression coefficient matrices in a GMANOVA-MANOVA model with normal error. The unique conditions for linear functions of the MLEs of regression coefficient matrices are presented, and the exact density functions or characteristic functions for these linear functions are derived. 相似文献
12.
A new class of type G selfdecomposable distributions on ℝ
d
is introduced and characterized in terms of stochastic integrals with respect to Lévy processes. This class is a strict subclass
of the class of type G and selfdecomposable distributions, and in dimension one, it is strictly bigger than the class of variance mixtures of normal
distributions by selfdecomposable distributions. The relation to several other known classes of infinitely divisible distributions
is established.
Research of J. Rosiński supported, in part, by a grant from the National Science Foundation. 相似文献
13.
B. Grigelionis 《Lithuanian Mathematical Journal》2008,48(1):61-69
Lévy processes with marginal relativistic α-stable distributions are described. Strictly stationary Ornstein-Uhlenbeck type processes with one-dimentional relativistic
α-stable distributions are constructed. The exponential family as Esscher transforms of distributions on D
[0,∞)(R
d
) of relativistic α-stable Lévy processes is obtained and the corresponding mixed exponential processes are characterized. 相似文献
14.
Empirical measures generated by random sequences with deterministic and random noises have same asymptotic distributions provided
that the noises have same asymptotic distributions (cf., Davydov and Zitikis, 2004, Proc. Am. Math. Soc. 132, 1203–1210). This phenomenon has raised an intriguing question about the possibility of distinguishing the two types of noises
based only on their asymptotic distributions. In the present paper we suggest an answer to the question by considering asymptotic
variances, and distributions, of the appropriately centered and normalized empirical measures and processes.
In final form 6 January 2005 相似文献
15.
In this paper, we propose approximations to compute the steady-state performance measures of the M/GI/N+GI queue receiving Poisson arrivals with N identical servers, and general service and abandonment-time distributions. The approximations are based on scaling a single
server M/GI/1+GI queue. For problems involving deterministic and exponential abandon times distributions, we suggest a practical way to compute
the waiting time distributions and their moments using the Laplace transform of the workload density function. Our first contribution
is numerically computing the workload density function in the M/GI/1+GI queue when the abandon times follow general distributions different from the deterministic and exponential distributions.
Then we compute the waiting time distributions and their moments. Next, we scale-up the M/GI/1+GI queue giving rise to our approximations to capture the behavior of the multi-server system. We conduct extensive numerical
experiments to test the speed and performance of the approximations, which prove the accuracy of their predictions.
相似文献
16.
N. Balakrishnan U. Kamps M. Kateri 《Annals of the Institute of Statistical Mathematics》2012,64(2):303-318
For general step-stress experiments with arbitrary baseline distributions, wherein the stress levels change immediately after
having observed pre-specified numbers of observations under each stress level, a sequential order statistics model is proposed
and associated inferential issues are discussed. Maximum likelihood estimators (MLEs) of the mean lifetimes at different stress
levels are derived, and some useful properties of the MLEs are established. Joint MLEs are also derived when an additional
location parameter is introduced into the model, and estimation under order restriction of the parameters at different stress
levels is finally discussed. 相似文献
17.
The M/PH/∞ system is introduced in this paper to analyze the superposition of a large number of data connections on an ATM link. In
this model, information is transmitted in bursts of data arriving at the link as a Poisson process of rate λ and burst durations
are PH distributed with unit mean. Some transient characteristics of the M/PH/∞ system, namely the duration θ of an excursion by the occupation process {Xt} above the link transmission capacity C, the area V swept under process {Xt} above C and the number of customers arriving in such an excursion period, are introduced as performance measures. Explicit methods
of computing their distributions are described. It is then shown that, as conjectured in earlier studies, random variables
Cθ,CV and N converge in distribution as C tends to infinity while the utilization factor of the link defined by γ = λ/C is fixed in (0,1), towards some transient characteristics of an M/M/1 queue with input rate γ and unit service rate. Further simulation results show that after adjustment of the load of the M/M/1 queue, a similar convergence result holds for the superposition of a large number of On/Off sources with various On and Off
period distributions. This shows that some transient quantities associated with an M/M/1 queue can be used in the characterization of open loop multiplexing of a large number of On/Off sources on an ATM link.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
18.
Diego Kuonen 《Computational Statistics》2005,20(2):231-244
Summary Saddlepoint methods can provide extremely accurate approximations to resampling distributions. This article applies them to
distributions of studentized bootstrap statistics based on robustM-estimates. As examples we consider the studentized versions of Huber’sM-estimate of location, of its initially MAD scaled version, and of Huber’s proposal 2. The studentized version of Huber’s
proposal 2 seems to be a preferable measure of location. Remarks on implementation and related problems are given. 相似文献
19.
LiangXiming LiFei XuChengxian 《高校应用数学学报(英文版)》2000,15(4):470-482
By using Fukushima‘s differentiable merit function,Taji,Fukushima and Ibaraki have given a globally convergent modified Newton method for the strongly monotone variational inequality problem and proved their method to be quadratically convergent under certain assumptions in 1993. In this paper a hybrid method for the variational inequality problem under the assumptions that the mapping F is continuously differentiable and its Jacobian matrix F(x) is positive definite for all x∈S rather than strongly monotone and that the set S is nonempty, polyhedral,closed and convex is proposed. Armijo-type line search and trust region strategies as well as Fukushima‘s differentiable merit function are incorporated into the method. It is then shown that the method is well defined and globally convergent and that,under the same assumptions as those of Taji et al. ,the method reduces to the basic Newton method and hence the rate of convergence is quadratic. Computational experiences show the efficiency of the proposed method. 相似文献
20.
The main focus in this paper is on homogenization of the parabolic problem ∂
t
uɛ − ∇ · (a(x/ɛ,t/ɛ,t/ɛ
r
)∇u
ɛ
) = f. Under certain assumptions on a, there exists a G-limit b, which we characterize by means of multiscale techniques for r > 0, r ≠ 1. Also, an interpretation of asymptotic expansions in the context of two-scale convergence is made. 相似文献