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91.
A new class of distributions for the microcanonical ensemble, which are shown to be stable laws, are derived by applying the central limit theorem to the canonical ensemble. This opens up a whole new host of phenomena that can be treated from a unified thermodynamic point of view. Pressure broadening of line shapes is used as an illustration.1. Work supported, in part, by contributions from the Consiglio Nazionale di Ricerche and the Ministero dell'Università e della Ricerca Scientifica e Tecnologica.2. The interaction parameterC is proportional to the mean square dipole moment. As an order of magnitude of the dipole moment, we can take it as the product of the electric charge and a typical atomic radius for a moderately excited state, which is several times the Bohr radius. Multiplication by the fine structure constant converts the Bohr radius into the Compton wavelength, thereby reducing the magnitude of the interaction by 1/137. 相似文献
92.
Sigeo Aki 《Annals of the Institute of Statistical Mathematics》1992,44(2):363-378
Let X
1, X
2,... be a sequence of nonnegative integer valued random variables.For each nonnegative integer i, we are given a positive integer k
i
. For every i = 0, 1, 2,..., E
i
denotes the event that a run of i of length k
i
occurs in the sequence X
1, X
2,.... For the sequence X
1, X
2,..., the generalized pgf's of the distributions of the waiting times until the r-th occurrence among the events % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% WaaiWabeaacaWGfbWaaSbaaSqaaiaadMgaaeqaaaGccaGL7bGaayzF% aaWaa0baaSqaaiaadMgacqGH9aqpcaaIWaaabaGaeyOhIukaaaaa!43D8!\[\left\{ {E_i } \right\}_{i = 0}^\infty\]are obtained. Though our situations are general, the results are very simple. For the special cases that X's are i.i.d. and {0, 1}-valued, the corresponding results are consistent with previously published results.This research was partially supported by the ISM Cooperative Research Program (90-ISM-CRP-11) of the Institute of Statistical Mathematics. 相似文献
93.
J. A. Cuesta-Albertos C. Matrán-Bea A. Tuero-Diaz 《Journal of Theoretical Probability》1996,9(2):263-283
We provide two families of lower bounds for theL
2-Wasserstein metric in separable Hilbert spaces which depend on the basis chosen for the space. Then we focus on one of these families and we provide a necessary and sufficient condition for the supremum in it to be attained. In the finite dimensional case, we identify the basis which provides the most accurate lower bound in the family.Research partially supported by the Spanish DGICYT under grants PB91-0306-02-00, 01 and 02. 相似文献
94.
This paper provides computable representations for the evaluation of the probability content of cones in isotropic random fields. A decomposition of quadratic forms in spherically symmetric random vectors is obtained and a representation of their moments is derived in terms of finite sums. These results are combined to obtain the distribution function of quadratic forms in spherically symmetric or central elliptically contoured random vectors. Some numerical examples involving the sample serial covariance are provided. Ratios of quadratic forms are also discussed. 相似文献
95.
M. Nussbaum 《Journal of multivariate analysis》1984,14(3):300-314
We consider estimation of the parameter B in a multivariate linear functional relationship Xi=ξi+ξ1i, Yi=Bξi+ξ2i, i=1,…,n, where the errors (ζ1i′, ζ2i′) are independent standard normal and (ξi, i
) is a sequence of unknown nonrandom vectors (incidental parameters). If there are no substantial a priori restrictions on the infinite sequence of incidental parameters then asymptotically the model is nonparametric but does not fit into common settings presupposing a parameter from a metric function space. A special result of the local asymptotic minimax type for the m.1.e. of B is proved. The accuracy of the normal approximation for the m.l.e. of order n−1/2 is also established. 相似文献
96.
Paul Deheuvels 《Journal of multivariate analysis》1983,13(2):257-272
A new model for point processes is developed which assumes that the interarrival times are exponentially distributed and follow joint multivariate extreme value distributions. It is shown that such processes may arise via natural generating procedures, and that, under very weak assumptions, that they can be approximated as closely as desired by appropriate finite models. 相似文献
97.
Wim Vervaat 《Stochastic Processes and their Applications》1973,1(4):317-334
Weak and strong functional limit theorems are obtained for record values and record epochs in a sequence of independent random variables with common distribution F. The emphasis is on the case in which F is concentrated on the non-negative integers. For contrast, the well-known case of continuous F is also considered. Analogues of results obtained earlier by Resnick, de Haan and the author for continuous F are presented here for F concentrated on the non-negative integers. Also is investigated under which circumstances the latter case is so close to the continuous F case that the resulting limit theorems are the same. 相似文献
98.
Moshe Shaked 《Annals of the Institute of Statistical Mathematics》1979,31(1):67-84
In this work we consider some familiar and some new concepts of positive dependence for interchangeable bivariate distributions.
By characterizing distributions which are positively dependent according to some of these concepts, we indicate real situations
in which these concepts arise naturally. For the various families of positively dependent distributions we prove some closure
properties and demonstrate all the possible logical relations. Some inequalities are shown and applied to determine whether
under- (or over-) estimates, of various probabilistic quantities, occur when a positively dependent distribution is assumed
(falsely) to be the product of its marginals (that is, when two positively dependent random variables are assumed, falsely,
to be independent). Specific applications in reliability theory, statistical mechanics and reversible Markov processes are
discussed.
This work was partially supported by National Science Foundation GP-30707X1. It is part of the author's Ph.D. dissertation
prepared at the University of Rochester and supervised by A. W. Marshall.
Now at Indiana University. 相似文献
99.
The spectroscopic amplitudes, form factors, angular distributions and total cross-sections for two nucleon transfer reactions
in Zr-region in the zero range distorted wave Born approximation are calculated using consistent set of shell model wave functions.
A single normalisation factor gives a good fit to all the two neutron transfer reaction data whereas the corresponding fit
for the two-proton transfer reaction data is less satisfactory. 相似文献
100.
Zbigniew J. Jurek 《Journal of multivariate analysis》1983,13(4):578-604
Let
= {Ut: t > 0} be a strongly continuous one-parameter group of operators on a Banach space X and Q be any subset of a set
(X) of all probability measures on X. By
(Q;
) we denote the class of all limit measures of {Utn(μ1 * μ2*…*μn)*δxn}, where {μn}Q, {xn}X and measures Utnμj (j=1, 2,…, n; N=1, 2,…) form an infinitesimal triangular array. We define classes Lm(
) as follows: L0(
)=
(
(X);
), Lm(
)=
(Lm−1(
);
) for m=1, 2,… and L∞(
)=m=0∞Lm(
). These classes are analogous to those defined earlier by Urbanik on the real line. Probability distributions from Lm(
), m=0, 1, 2,…, ∞, are described in terms of their characteristic functionals and their generalized Poisson exponents and Gaussian covariance operators. 相似文献