共查询到20条相似文献,搜索用时 46 毫秒
1.
In this paper, we investigate the exact distribution of the waiting time for ther-th ℓ-overlapping occurrence of success-runs of a specified length in a sequence of two state Markov dependent trials. The
probability generating functions are derived explicitly, and as asymptotic results, relationships of a negative binomial distribution
of orderk and an extended Poisson distribution of orderk are discussed. We provide further insights into the run-related problems from the viewpoint of the ℓ-overlapping enumeration
scheme. We also study the exact distribution of the number of ℓ-overlapping occurrences of success-runs in a fixed number
of trials and derive the probability generating functions. The present work extends several properties of distributions of
orderk and leads us a new type of geneses of the discrete distributions. 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.
Filipe J. Marques M. Theodor Loots Andriëtte Bekker 《Mathematical Methods in the Applied Sciences》2019,42(17):5718-5735
Series representations for several density functions are obtained as mixtures of generalized gamma distributions with discrete mass probability weights, by using the exponential expansion and the binomial theorem. Based on these results, approximations based on mixtures of generalized gamma distributions are proposed to approximate the distribution of the sum of independent random variables, which may not be identically distributed. The applicability of the proposed approximations are illustrated for the sum of independent Rayleigh random variables, the sum of independent gamma random variables, and the sum of independent Weibull random variables. Numerical studies are presented to assess the precision of these approximations. 相似文献
4.
Sigeo Aki Hisataka Kuboki Katuomi Hirano 《Annals of the Institute of Statistical Mathematics》1984,36(1):431-440
Summary This paper gives some results on calculation of probabilities and moments of the discrete distributions of orderk. Further, a new distribution of orderk, which is called the logarithmic series distribution of orderk, is investigated. Finally, we discuss the meaning of theorder of the distributions.
The Institute of Statistical Mathematics 相似文献
5.
Tomasz J. Kozubowski 《Annals of the Institute of Statistical Mathematics》2000,52(2):231-238
We show that every strictly geometric stable (GS) random variable can be represented as a product of an exponentially distributed random variable and an independent random variable with an explicit density and distribution function. An immediate application of the representation is a straightforward simulation method of GS random variables. Our result generalizes previous representations for the special cases of Mittag-Leffler and symmetric Linnik distributions. 相似文献
6.
Joint distributions of numbers of success runs of specified lengths in linear and circular sequences
In this paper, we study two joint distributions of the numbers of success runs of several lengths in a sequence ofn Bernoulli trials arranged on a line (linear sequence) or on a circle (circular sequence) based on four different enumeration
schemes. We present formulae for the evaluation of the joint probability functions, the joint probability generating functions
and the higher order moments of these distributions. Besides, the present work throws light on the relation between the joint
distributions of the numbers of success runs in the circular and linear binomial model. We give further insights into the
run-related problems arisen from the circular sequence. Some examples are given in order to illustrate our theoretical results.
Our results have potential applications to other problems such as statistical run tests for randomness and reliability theory.
This research was partially supported by the ISM Cooperative Research Program (2003-ISM.CRP-2007). 相似文献
7.
Lars Holst 《Extremes》2001,4(2):129-145
Take n independent copies of a strictly positive random variable X and divide each copy with the sum of the copies, thus obtaining n random probabilities summing to one. These probabilities are used in independent multinomial trials with n outcomes. Let N
n(N
*
n) be the number of trials needed until each (some) outcome has occurred at least c times. By embedding the sampling procedure in a Poisson point process the distributions of N
n and N
*
n
can be expressed using extremes of independent identically distributed random variables. Using this, asymptotic distributions as n are obtained from classical extreme value theory. The limits are determined by the behavior of the Laplace transform of X close to the origin or at infinity. Some examples are studied in detail. 相似文献
8.
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
9.
Kenneth Lange Janet S. Sinsheimer 《Journal of computational and graphical statistics》2013,22(2):175-198
Abstract Maximum likelihood estimation with nonnormal error distributions provides one method of robust regression. Certain families of normal/independent distributions are particularly attractive for adaptive, robust regression. This article reviews the properties of normal/independent distributions and presents several new results. A major virtue of these distributions is that they lend themselves to EM algorithms for maximum likelihood estimation. EM algorithms are discussed for least Lp regression and for adaptive, robust regression based on the t, slash, and contaminated normal families. Four concrete examples illustrate the performance of the different methods on real data. 相似文献
10.
Tom Leonard John S. J. Hsu Kam-Wah Tsui James F. Murray 《Annals of the Institute of Statistical Mathematics》1994,46(2):203-220
Equally weighted mixture models are recommended for situations where it is required to draw precise finite sample inferences requiring population parameters, but where the population distribution is not constrained to belong to a simple parametric family. They lead to an alternative procedure to the Laird-DerSimonian maximum likelihood algorithm for unequally weighted mixture models. Their primary purpose lies in the facilitation of exact Bayesian computations via importance sampling. Under very general sampling and prior specifications, exact Bayesian computations can be based upon an application of importance sampling, referred to as Permutable Bayesian Marginalization (PBM). An importance function based upon a truncated multivariatet-distribution is proposed, which refers to a generalization of the maximum likelihood procedure. The estimation of discrete distributions, by binomial mixtures, and inference for survivor distributions, via mixtures of exponential or Weibull distributions, are considered. Equally weighted mixture models are also shown to lead to an alternative Gibbs sampling methodology to the Lavine-West approach. 相似文献
11.
Grzegorz A. Rempala 《Proceedings of the American Mathematical Society》2004,132(1):261-272
By considering the variance formula for a shifted reciprocal of a binomial proportion, the asymptotic expansions of any order for first negative moments of binomial and negative binomial distributions truncated at zero are obtained. The expansions are given in terms of the factorial powers of the number of trials . The obtained formulae are more accurate than those of Marciniak and Wesoowski (1999) and simpler, as they do not involve the Eulerian polynomials.
12.
We consider the approximation of the convolution product of not necessarily identical probability distributions q
j
I + p
j
F, (j=1,...,n), where, for all j, p
j
=1−q
j
∈[0, 1], I is the Dirac measure at point zero, and F is a probability distribution on the real line. As an approximation, we use a compound binomial distribution, which is defined
in a one-parametric way: the number of trials remains the same but the p
j
are replaced with their mean or, more generally, with an arbitrary success probability p. We also consider approximations by finite signed measures derived from an expansion based on Krawtchouk polynomials. Bounds
for the approximation error in different metrics are presented. If F is a symmetric distribution about zero or a suitably shifted distribution, the bounds have a better order than in the case
of a general F. Asymptotic sharp bounds are given in the case, when F is symmetric and concentrated on two points.
An erratum to this article can be found at 相似文献
13.
John Panaretos Evdokia Xekalaki 《Annals of the Institute of Statistical Mathematics》1986,38(1):223-231
Summary The binomial and multinomial distributions are, probably, the best known distributions because of their vast number of applications.
The present paper examines some generalizations of these distributions with many practical applications. Properties of these
generalizations are studied and models giving rise to them are developed. Finally, their relationship to generalized Poisson
distributions is examined and limiting cases are given. 相似文献
14.
Kumi Yasuda 《Journal of Theoretical Probability》2000,13(3):635-657
Our aim in this paper is to characterize some classes of infinitely divisible distributions on locally compact abelian groups. Firstly infinitely divisible distributions with no idempotent factor on locally compact abelian groups are characterized by means of limit distributions of sums of independent random variables. We introduce semi-selfdecomposable distributions on topological fields, and in case of totally disconnected fields we give a limit theorem for them. We also give a characterization of semistable laws on p-adic field and show that semistable processes are constructed as scaling limits of sums of i.i.d. 相似文献
15.
Masayuki Uchida 《Annals of the Institute of Statistical Mathematics》1998,50(3):587-601
Let X-m+1, X-m+2,..., X0, X1, X2,..., Xn be a time-homogeneous {0, 1}-valued m-th order Markov chain. The probability distributions of numbers of runs of "1" of length k (k m) and of "1" of length k (k < m) in the sequence of a {0, 1}-valued m-th order Markov chain are studied. There are some ways of counting numbers of runs with length k. This paper studies the distributions based on four ways of counting numbers of runs, i.e., the number of non-overlapping runs of length k, the number of runs with length greater than or equal to k, the number of overlapping runs of length k and the number of runs of length exactly k. 相似文献
16.
17.
This paper investigates a discrete‐time risk model that involves exchangeable dependent loss generating claim occurrences and compound binomially distributed aggregate loss amounts. First, a general framework is presented to derive the distribution of a surplus sequence using the model. This framework is then applied to obtain the distribution of any function of a surplus sequence in a finite‐time interval. Specifically, the distribution of the maximum surplus is obtained under nonruin conditions. Based on this distribution, the computation of the minimum surplus distribution is given. Asset and risk management–oriented implications are discussed for the obtained distributions based on numerical evaluations. In addition, comparisons are made involving the corresponding results of the classical discrete‐time compound binomial risk model, for which claim occurrences are independent and identically distributed. 相似文献
18.
In this paper, we study the compound binomial model in Markovian environment, which is proposed by Cossette, et al. (2003).
We obtain the recursive formula of the joint distributions of T, X(T − 1) and |X(T)| (i.e., the time of ruin, the surplus before ruin and the deficit at ruin) by the method of mass function of up-crossing
zero points, as given by Liu and Zhao (2007). By using the same method, the recursive formula of supremum distribution is
obtained. An example is included to illustrate the results of the model. 相似文献
19.
Jonathan M. Kane 《Proceedings of the American Mathematical Society》2001,129(7):2127-2133
The approach to limits guaranteed by the Central Limit Theorem appears to be monotonic in many cases. A variety of empirical examples are discussed. Proofs are given for some special cases of the binomial, gamma, and Poisson distributions.
20.
Ewa Marciniak Jacek Wesolowski 《Proceedings of the American Mathematical Society》1999,127(11):3329-3338
Asymptotic expansions of any order for expectations of inverses of random variables with positive binomial and negative binomial distributions are obtained in terms of the Eulerian polynomials. The paper extends and improves upon an expansion due to David and Johnson (1956-7).