排序方式: 共有59条查询结果,搜索用时 15 毫秒
31.
We introduce the notion of random self-decomposability and discuss its relation to the concepts of self-decomposability and geometric infinite divisibility. We present its connection with time series autoregressive schemes with a regression coefficient that randomly turns on and off. In particular, we provide a characterization of random self-decomposability as well as that of marginal distributions of stationary time series that follow this scheme. Our results settle an open question related to the existence of such processes. 相似文献
32.
The paper discusses recent advances in the theory of multivariate geometric stable (GS) distributions. The results presented include characterizations, mixture representations, properties, simulation, and estimation. 相似文献
33.
We establish precise logarithmic asymptotics around the origin for the Le´vy measure of geometric stable (GS) random variables. This implies, in particular, exponential rate of convergence in series representation of GS random variables. 相似文献
34.
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
35.
Let {Xi, i1} be a sequence of i.i.d. random vectors inRd, and letνp, 0<p<1, be a positive, integer valued random variable, independent ofXis. Theν-stable distributions are the weak limits of properly normalized random sums ∑νpi=1 Xiasνp
∞ andpνp
ν. We study the properties ofν-stable laws through their representation via stable laws. In particular, we estimate their tail probabilities and provide conditions for finiteness of their moments. 相似文献
36.
Tomasz J. Kozubowski Anna K. Panorska Krzysztof Podgrski 《Journal of multivariate analysis》2008,99(7):1418-1437
The joint distribution of X and N, where N has a geometric distribution and X is the sum of N IID exponential variables (independent of N), is infinitely divisible. This leads to a bivariate Lévy process {(X(t),N(t)),t≥0}, whose coordinates are correlated negative binomial and gamma processes. We derive basic properties of this process, including its covariance structure, representations, and stochastic self-similarity. We examine the joint distribution of (X(t),N(t)) at a fixed time t, along with the marginal and conditional distributions, joint integral transforms, moments, infinite divisibility, and stability with respect to random summation. We also discuss maximum likelihood estimation and simulation for this model. 相似文献
37.
This paper obtains solitons as well as other solutions to a few nonlinear evolution equations that appear in various areas of mathematical physics. The two analytical integrators that are applied to extract solutions are tan–cot method and functional variable approaches. The soliton solutions can be used in the further study of shallow water waves in (1+1) as well as (2+1) dimensions. 相似文献
38.
Samuel Kotz Tomasz J. Kozubowski Krzysztof Podgórski 《Annals of the Institute of Statistical Mathematics》2002,54(4):816-826
Maximum likelihood estimators (MLE's) are presented for the parameters of a univariate asymmetric Laplace distribution for all possible situations related to known or unknown parameters. These estimators admit explicit form in all but two cases. In these exceptions effective algorithms for computing the estimators are provided. Asymptotic distributions of the estimators are given. The asymptotic normality and consistency of the MLE's for the scale and location parameters are derived directly via representations of the relevant random variables rather than from general sufficient conditions for asymptotic normality of the MLE's. 相似文献
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