共查询到20条相似文献,搜索用时 21 毫秒
1.
N. G. Ushakov 《Journal of Mathematical Sciences》1998,91(3):3008-3013
Characterizations of discrete unimodality are studied. They are applied to prove some criteria for characteristic functions
of discrete unimodal distributions and to obtain a discrete analogue of the Gauss inequality.
Proceedings of the Seminar on Stability Problems for Stochastic Models, Moscow, Russia. 1996. Part II. 相似文献
2.
Summary The class of discrete distributions of orderk is defined as the class of the generalized discrete distributions with generalizer a discrete distribution truncated at zero
and from the right away fromk+1. The probability function and factorial moments of these distributions are expressed in terms of the (right) truncated
Bell (partition) polynomials and several special cases are briefly examined. Finally a Poisson process of orderk, leading in particular to the Poisson distribution of orderk, is discussed. 相似文献
3.
The problem of estimating the mode of a discrete distribution is considered. New characterizations of discrete unimodal and
multi-modal distributions are obtained. The proposed mode estimator is essentially the sample mode, modulo appropriate modifications
when the sample mode is not well defined. In the case of i.i.d. observations coming from a unimodal discrete distribution,
our proposed mode estimator is shown to possess a number of strong asymptotic properties. Many of these results extend to
the case of multi-modal discrete distributions as well. Our method also applies — and we have similar asymptotic results —
to the problem of mode estimation based on finitely many observations on a Markov chain whose equilibrium distribution is
the underlying unimodal distribution. For unimodal discrete distributions, we also propose a consistent large sample test
of mode based on the proposed statistic. Applications of mode estimation problem in Monte-Carlo optimization problem using
the Hastings Metropolis chain and in prediction problem using binary response variable, specially in the context of dose-response
experiments, are also illustrated. 相似文献
4.
R. M. Korwar 《Annals of the Institute of Statistical Mathematics》1989,41(2):305-321
This paper deals with a new system of discrete distributions. It also gives several characterizations of the Waring (and hence the Yule) distribution (and its truncated versions), the super-Poisson, the discrete uniform and other discrete distributions by using this system and other such systems existing in the literature, and linear regression. Continuous analogues of the above results are also briefly discussed. 相似文献
5.
Yanyuan Ma Marc G. Genton Emanuel Parzen 《Annals of the Institute of Statistical Mathematics》2011,63(2):227-243
The asymptotic distribution of sample quantiles in the classical definition is well-known to be normal for absolutely continuous
distributions. However, this is no longer true for discrete distributions or samples with ties. We show that the definition
of sample quantiles based on mid-distribution functions resolves this issue and provides a unified framework for asymptotic
properties of sample quantiles from absolutely continuous and from discrete distributions. We demonstrate that the same asymptotic
normal distribution result as for the classical sample quantiles holds at differentiable points, whereas a more general form
arises for distributions whose cumulative distribution function has only one-sided differentiability. For discrete distributions
with finite support, the same type of asymptotics holds and the sample quantiles based on mid-distribution functions either
follow a normal or a two-piece normal distribution. We also calculate the exact distribution of these sample quantiles for
the binomial and Poisson distributions. We illustrate the asymptotic results with simulations. 相似文献
6.
Beda Chan 《Insurance: Mathematics and Economics》1982,1(4):241-243
We apply power series techniques for differential equations on probability generating functions to derive recursive formulas for discrete compound distributions. Such formulas are computationally effective and useful in risk theory. 相似文献
7.
《Insurance: Mathematics and Economics》2006,38(2):391-405
In this paper we consider some widely utilized classes of discrete distributions and aim to provide a systematic overview about their preservation under convolution and mixing. Moreover, inclusion properties among these classes are discussed. This paper will serve as a detailed reference for the study and applications of the preservation of the classes of discrete distributions. 相似文献
8.
Yann Gudon 《商业与工业应用随机模型》1999,15(3):195-224
We propose a computational approach for implementing discrete hidden semi-Markov chains. A discrete hidden semi-Markov chain is composed of a non-observable or hidden process which is a finite semi-Markov chain and a discrete observable process. Hidden semi-Markov chains possess both the flexibility of hidden Markov chains for approximating complex probability distributions and the flexibility of semi-Markov chains for representing temporal structures. Efficient algorithms for computing characteristic distributions organized according to the intensity, interval and counting points of view are described. The proposed computational approach in conjunction with statistical inference algorithms previously proposed makes discrete hidden semi-Markov chains a powerful model for the analysis of samples of non-stationary discrete sequences. Copyright © 1999 John Wiley & Sons, Ltd. 相似文献
9.
Kam-Wah Tsui 《Annals of the Institute of Statistical Mathematics》1986,38(1):45-56
Summary In multiparameter estimation for multivariate discrete distributions with infinite support, inadmissibility problems in situations
where the multivariate probability distribution function isnot a product of the one-dimensional marginal probability distribution functions have previously been unexplored. This paper
examines the inadmissibility problem in some of these situations. Special attention is given to estimating the mean of a negative
multinomial distribution. In estimating the mean vector, certain Clevenson-Zidek type estimators are shown to be uniformly
better than the usual estimator under a large class of generally scaled squared loss functions. Some of the results are generalized
to other multivariate discrete distributions and to situations where several independent negative multinomial distributions
are considered. 相似文献
10.
Most work on conditionally specified distributions has focused on approaches that operate on the probability space, and the constraints on the probability space often make the study of their properties challenging. We propose decomposing both the joint and conditional discrete distributions into characterizing sets of canonical interactions, and we prove that certain interactions of a joint distribution are shared with its conditional distributions. This invariance opens the door for checking the compatibility between conditional distributions involving the same set of variables. We formulate necessary and sufficient conditions for the existence and uniqueness of discrete conditional models, and we show how a joint distribution can be easily computed from the pool of interactions collected from the conditional distributions. Hence, the methods can be used to calculate the exact distribution of a Gibbs sampler. Furthermore, issues such as how near compatibility can be reconciled are also discussed. Using mixed parametrization, we show that the proposed approach is based on the canonical parameters, while the conventional approaches are based on the mean parameters. Our advantage is partly due to the invariance that holds only for the canonical parameters. 相似文献
11.
Distribution-free newsvendor models often assume continuous demand distributions to facilitate analysis and computation. However, in practice, discrete demand is a natural phenomenon. So far, there exists no analytical and computational results in the literature under this setting. Thus, the goal of this paper is to investigate the newsvendor problems with partial information when the demand is discrete and solve them using the so-called discrete moment problems. Numerical results are presented to illustrate the value of discrete information.
相似文献12.
For a wide class of discrete distributions, we derive a representation of the inverse (negative) moments through the Stirling numbers of the first kind and inverse factorial moments. We specialize the results for the Poisson, binomial, hypergeometric and negative binomial distributions. 相似文献
13.
Udo Krzensk 《Computational Statistics》2004,19(4):535-550
Summary This paper deals with the computation of exact cumulative probabilities of discrete distributions and its inverses. For the
computation of cumulative probabilities an efficient and universal algorithm of 15 lines is presented, which can be applied
to the most important discrete distributions (e.g. the binomial, the poisson and the hypergeometric distribution). With a
slight modification an algorithm of 20 lines is obtained for the calculation of the respective inverse distributions. The
accuracy of both algorithms can be specified. Both algorithms are simple, very fast and numerically stable even if the sample
size is one billion. 相似文献
14.
15.
《Statistics & probability letters》1988,6(6):379-382
The convenient sufficient conditions for the infinite divisibility of discrete distributions are generalized. A numerical example is presented. The role of infinitely divisible distributions in applications is discussed. 相似文献
16.
Kenneth S. Berenhaut John V. Baxley Robert G. Lyday 《Statistics & probability letters》2011,81(12):1940-1944
In this note, we consider a question of Móri regarding estimating the deviation of the kth terms of two discrete probability distributions in terms of the supremum distance between their generating functions over the interval [0,1]. An optimal bound for distributions on finite support is obtained. Properties of Chebyshev polynomials are employed. 相似文献
17.
《Insurance: Mathematics and Economics》1988,7(4):283-285
In the present note we give a recursive algorithm for convolutions of discrete uniform distributions. 相似文献
18.
19.
This paper considers estimating parameters in the discrete distributions of order k such as the binomial, the geometric, the Poisson and the logarithmic series distributions of order k. It is discussed how to calculate maximum likelihood estimates of parameters of the distributions based on independent observations. Further, asymptotic properties of estimators by the method of moments are investigated. In some cases, it is found that the values of asymptotic efficiency of the moment estimators are surprisingly close to one. 相似文献
20.
A. R. Kamat 《Annals of the Institute of Statistical Mathematics》1965,17(1):287-293
Summary This note describes an interesting property of the mean deviation which holds for a number of commonly known discrete distributions.
The property is also examined for some of the well-known continuous distributions. 相似文献