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1.
Quasi-maximum likelihood histogram sieve estimators of the intensity function of an indirectly observed Poisson process are studied. The setup differs from the standard one in that the exact form of the folding operator may not be known. Instead, approximate knowledge on its discretized version is available. Conditions for strong L 2-consistency are given and admissible discretization rates are studied. In non-folding problems, the number of histogram bins may essentially increase at the usual maximal rate while folding reduces the allowed discretization rates. It is shown that, even in moderately ill-posed problems, the discretization effects may be critical for the strong L 2-convergence and that there is an essential need both for further regularization and for imposing stronger conditions on the estimated function. Not surprisingly, the most restrictive factor is the low approximation power of piecewise constant functions. A regularization method is proposed which suitably modifies the discrete approximation of the folding operator and ensures the strong consistency. Since no penalty term is being introduced, the EM algorithm can be used in its factorized, efficient form. Convergence rates are obtained in terms of the discrete problem. Received: July 1999  相似文献   

2.
In this paper, the maximum likelihood predictor (MLP) of the kth ordered observation, t k, in a sample of size n from a two-parameter exponential distribution as well as the predictive maximum likelihood estimators (PMLE's) of the location and scale parameters, θ and β, based on the observed values t r, …, t s (1≤rs<kn), are obtained in closed forms, contrary to the belief they cannot be so expressed. When θ is known, however, the PMLE of β and MLP of t k do not admit explicit expressions. It is shown here that they exist and are unique; sharp lower and upper bounds are also provided. The derived predictors and estimators are reasonable and also have good asymptotic properties. As applications, the total duration time in a life test and the failure time of a k-out-of-n system may be predicted. Finally, an illustrative example is included. Received: August 1999  相似文献   

3.
A new unbiased consistent asymptotically normal estimator U k of the intensity λ of a stationary multivariate Poisson point process is exhibited. This estimate is based on a combination of the j -th nearest neighbor (possibly non Euclidean) distances ( j =1, ..., k ) to a single fixed site x . A simple closed form containing logarithmic terms is obtained for E ( U l k )(0< l < k ).  相似文献   

4.
Abstract A displaced Poisson process is presented as a reasonable model in describing the stages of certain chronic diseases. Although in some respects the model is an oversimplification of the true picture its feature is that it facilitates the easy estimation of some of the important parameters that arise in this area. Among the quantities estimated are the mean lead time and the distribution function of the time spent in the preclinical state. Properties of some of the estimators are obtained.  相似文献   

5.
文章介绍了泊松积分在正态分布、二维正态分布、对数正态分布等问题中常见的应用,并给出了具体的例子。  相似文献   

6.
文章介绍了泊松积分在正态分布、二维正态分布、对数正态分布等问题中常见的应用,并给出了具体的例子。  相似文献   

7.
Tadeusz Bednarski 《Metrika》2002,55(1-2):27-36
An estimation method is presented which compromises robust efficiency with computational feasibility in the case of the generalized Poisson model. The formal setup is built on flexible nonparametric extensions of the underlying model. The estimation efficiency is expressed via minimax properties of tests resulting from expansions of estimators. The nonparametric neighborhoods related to the proposed score function are exemplified and a real data case is analysed. The resulting method balances several qualitative features of statistical inference: strong differentiability (asymptotic derivations are more accurate), efficiency and natural model extension (quality of formal basic assumptions).  相似文献   

8.
Summary A general model in fluctuations of sums of random variables leading, under certain assumptions, to each of the generalized and linear function Poisson, binomial and negative binomial distributions is presented. Moreover the generating functions and the factorial moments of the linear function Poisson, binomial and negative binomial distributions are obtained in close forms and certain distributional properties are discussed.  相似文献   

9.
Asymptotic normality and quick consistency of quasi-maximum likelihood estimators of parameters in a multivariate Poisson process are proved. Possible application of the results obtained to the problem of unfolding histograms is briefly discussed.  相似文献   

10.
Bernhard Klar 《Metrika》2000,52(3):237-252
Smooth tests are frequently used for testing the goodness of fit of a parametric family of distributions. One reason for the popularity of the smooth tests are the diagnostic properties commonly attributed to them. In recent years, however, it has been realized that these tests are strictly non-diagnostic when used conventionally. The paper examines how the smooth test statistics must be rescaled in order to obtain procedures having diagnostic properties at least for large sample sizes. Received: September 1999  相似文献   

11.
杜海霞 《价值工程》2014,(29):289-290
以n重贝努里概型为基础,利用极限分布,讨论了概率论中最常见的二项分布、泊松分布、指数分布、正态分布之间的关系,从而得到n重贝努里概型贯穿概率论教程的结论。  相似文献   

12.
The main purpose of this paper is to indicate formal theorems and conditions for the extensions of Rice's Formula for intensities of crossings of a fixed level u by a stationary process X(t) in order to provide the conditional (Palm) distribution of an associated process Y(t) at the level crossing instants. Sections 1 and 2 provide brief background material on Rice's Formula and Palm distributions, while relevant historical comments and basic results are given in Section 3. These are stated with some indications of proof in Section 4 and calculation of the Palm distributions shown in Section 5. Two cases of importance in applications are considered: (a) where (roughly) X(t) , Y(t) and the derivative X'(t) have a joint density and (b) where Y(t) = X'(t) . The resulting Palm distributions are each absolutely continuous with readily calculable densities. These are evaluated for Gaussian processes in Section 6 and applications to motivating 2 structural safety questions indicated in Section 7.  相似文献   

13.
S. K. Bar-Lev  P. Enis 《Metrika》1992,39(1):165-175
Summary Two parametric sets of normalizing transformations for the compound Poisson process are considered. The transformations in the first set are also variance stabilizing, and the optimum variance stabilizing transformation and an optimum normalizing transformation in this set are determined. The second set consists of power transformations, and an optimum normalizing transformation is obtained. Some comparisons with respect to normalization are made between these optimum transformations. The work of this author was performed while he was a visitor at the Department of Statistics, State University of New York at Buffalo.  相似文献   

14.
陈有锋  薛红  刘达卓 《价值工程》2011,30(31):144-145
本文主要讨论了由分数布朗运动和Poisson过程驱动的随机微分方程。当方程的系数满足Lipschitz条件和线性增长条件时,给出方程解的存在性和唯一性定理。  相似文献   

15.
We use the independence of the integer and fractional parts of exponentially distributed random variables to obtain expressions for the order statistics from a geometric distribution. As our main result we show that a strong form of this independence characterizes the exponential distribution.  相似文献   

16.
The particles distributed according to a Poisson random field execute independent critical branching Wiener processes. It looks natural that the largest empty ball around the origin becomes larger and larger with time. The asymptotic behaviour of the radius of the largest empty ball is studied.  相似文献   

17.
A Bayesian-like estimator of the process capability index Cpmk   总被引:1,自引:0,他引:1  
W. L. Pearn  G. H. Lin 《Metrika》2003,57(3):303-312
Pearn et al. (1992) proposed the capability index Cpmk, and investigated the statistical properties of its natural estimator for stable normal processes with constant mean μ. Chen and Hsu (1995) showed that under general conditions the asymptotic distribution of is normal if μ≠m, and is a linear combination of the normal and the folded-normal distributions if μ=m, where m is the mid-point between the upper and the lower specification limits. In this paper, we consider a new estimator for stable processes under a different (more realistic) condition on process mean, namely, P (μ≥m)=p, 0≤p≤1. We obtain the exact distribution, the expected value, and the variance of under normality assumption. We show that for P (μ≥m)=0, or 1, the new estimator is the MLE of Cpmk, which is asymptotically efficient. In addition, we show that under general conditions is consistent and is asymptotically unbiased. We also show that the asymptotic distribution of is a mixture of two normal distributions. RID="*" ID="*"  The research was partially supported by National Science Council of the Republic of China (NSC-89-2213-E-346-003).  相似文献   

18.
It is well–known that the fractional part and integer part of an exponentially distributed random variable are independent. Under some regularity conditions, the independence of the fractional part and integer part of a positive random variable characterizes the exponential distribution.  相似文献   

19.
Some properties of a first-order integer-valued autoregressive process (INAR)) are investigated. The approach begins with discussing the self-decomposability and unimodality of the 1-dimensional marginals of the process {Xn} generated according to the scheme Xn=α° X n-i +en, where α° X n-1 denotes a sum of Xn - 1, independent 0 - 1 random variables Y(n-1), independent of X n-1 with Pr -( y (n - 1)= 1) = 1 - Pr ( y (n-i)= 0) =α. The distribution of the innovation process ( e n) is obtained when the marginal distribution of the process ( X n) is geometric. Regression behavior of the INAR(1) process shows that the linear regression property in the backward direction is true only for the Poisson INAR(1) process.  相似文献   

20.
The truncated Poisson regression model is used to arrive at point and interval estimates of the size of two offender populations, i.e. drunk drivers and persons who illegally possess firearms. The dependent capture–recapture variables are constructed from Dutch police records and are counts of individual arrests for both violations. The population size estimates are derived assuming that each count is a realization of a Poisson distribution, and that the Poisson parameters are related to covariates through the truncated Poisson regression model. These assumptions are discussed in detail, and the tenability of the second assumption is assessed by evaluating the marginal residuals and performing tests on overdispersion. For the firearms example, the second assumption seems to hold well, but for the drunk drivers example there is some overdispersion. It is concluded that the method is useful, provided it is used with care.  相似文献   

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