Showing papers on "Natural exponential family published in 1991"

Exponential sums and Goppa codes. I

Abstract: A bound is obtained which generalizes the Carlitz-Uchiyama result, based on a theorem of Bombieri and Weil about exponential sums. This new bound is used to estimate the covering radius of long binary Goppa codes. A new lower bound is also derived on the minimum distance of the dual of a binary Goppa code, similar to that for BCH codes. This is an example of the use of a number-theory bound for the problem of the estimation of minimum distance of codes, as posed in research problem 9.9 of Mac Williams and Sloane, The Theory of Error Correcting Codes.

On the hyper-Dirichlet type 1 and hyper-Liouville distributions

Abstract: This paper concerns the characterization of a new family of multivariate beta distribution functions - the hyper-Dirichlet type 1 distribution. This family describes the joint density function of the terminal variates of an arbitrary tree constructed from finite sequences of probability vectors having independent Dirichlet type 1 distributions. Expressions for the general properties of the hyper-Dirichlet type 1 distribution are presented. In addition, the hyper-Liouville distribution is described and its properties are discussed as well as a generalization of the Liouville integral identity.

Construction of exponential tension B-splines of arbitrary order

Abstract: Some results for exponential B-splines in tension are extended to higher order exponential B-splines Based on a differentiation formula we derive a Bernstein/Bezier like representation on each interval

A general recurrence relation for moments of order statistics in a class of probability distributions and characterizations

Abstract: In a class of distribution functions, including exponential, power function, Pareto, Lomax, and logistic distributions, a general recurrence relation for moments of order statistics is given. The validity of this identity for certain constants and some sequence of order statistics leads to characterizations of probability distributions. Several recurrence relations and characterization results known from the literature are particular cases of the theorems stated.

Gamma Duration Models with Heterogeneity

Abstract: In the authors' analysis of nonwork spells for Workers Compensation Insurance, they use the family of generalized gamma distributions for the structural model of failure time and both nonparametric and parametric controls for heterogeneity. These specifications allow for nested likelihood tests of not only the correct form for parametric heterogeneity, but for the structural distributions as well. The authors find in their data that while heterogeneity is important, both parametric and nonparametric types of control do about equally well. The "best" (in terms of statistical fit) structural distribution is the generalized gamma function; the exponential distribution fits especially poorly. Copyright 1991 by MIT Press.

Empirical input distributions: an alternative to standard input distributions in simulation modeling

Abstract: The authors investigate the effect of input-distribution specification on the validity of output from simple queuing models. In particular, the use of various kinds of empirical distributions for approximating service-time distributions is studied. It is shown that, when the approximating distributions were compared on the basis of variance and bias in their estimates, the empirical distributions generally did as well as the best fitted standard distributions, and sometimes better. For example, when Weibull was the true distribution, the fitted Weibull and gamma were the best fitting distributions among the standard distributions, with the least bias and variance. The empirical distributions were a good match where both the criteria were concerned, and in some cases had lower variance and bias. >

Hierarchical baxes predictive means and variances with application to sample survey inference

Abstract: Samples are observed from k populations having means ,(i and distributed according to a natural exponential family with quadratic variance function (NEF-QVF). Assuming an exchangeable two-stage prior, conjugate at the first stage, formulas for posterior means, variances and covariances of the μi are expressed in a unified way for all NEF-QVF models in terms of integrals over the posterior density of the two hyperparameters. This posterior density is expressed simply in terms of the normalizing function for the conjugate prior.Posterior predictive means and variances for averages of new observations are also obtained. These formulas are applied, with very little effort, to the finite population situation where the samples are independent simple random samples from the k populations, and where an exchangeable NEF-QVF superpopulation model is assumed. Posterior (predictive) means and variances for finite population totals, means and proportions are obtained. These results are illustrated with an application ...

On a modified test of equality of scale parameters of exponential distributions

Abstract: In this paper, an exact distribution of a modifier likelihood ratio criterion for testing the equality of scale parameters of several two parameter exponential distributions is obtained for the case of unequal sample size in a computational form. A short table of critical values of the proposed statistic is also presented.

Derivation of exponential joint probability distributions of structure factors in P1 with maximum entropy and irreducible cluster integrals

Abstract: Recently the application of the maximum-entropy method to direct methods has been initiated for a priori uniformly and independently distributed atoms, introducing non-uniformity in direct space by putting constraints on the expected values of the distribution [Bricogne (1984). Acta Cryst. A40, 410–445; (1988). Acta Cryst. A44, 517–545]. In this paper a start is made in using the maximum-entropy principle for deriving exponential joint probability distributions of structure factors for a chemically more realistic model of a priori non-uniformly and non-independently distributed atoms. The maximum-entropy equations are obtained by treating the atomic positions as well as the reciprocal vectors as random variables and applying constraints on the maximum of the distribution. The interdependence of the Lagrange multipliers leads to inequalities which may be compared with the Karle–Hauptman inequalities. The radial interatomic correlations such as minimal interatomic distances lead to integrals whose evaluation via the cluster integral mechanism is shown to be equivalent to those of the classical hard-sphere gas in an external field [Van Kampen (1961). Physica (Utrecht), 27, 783–792]. The Debye scattering equation results from these calculations. The exponential multiplet terms are expressed as cluster integrals. From the distribution of the single structure factor the influence of the interatomic correlations on the normalization procedure is assessed. The exponential triplet distribution up to order N−3/2 is derived and is shown to be in agreement with the exponential Edgeworth result [Karle & Gilardi (1973). Acta Cryst. A29, 401–407]. The effect of the radial interatomic correlations on the triplet distribution is discussed. The exponential quartet distribution up to order N−1 is derived, and found to be equal to the well known result [Hauptman (1975). Acta Cryst. A31, 617–679, 680–687] except for some normalization terms resulting from the interatomic correlations.

Characterizations of exponential distributions within the life distribution classes

Abstract: Within different life distribution classes, we discuss characterization of exponential distributions based on moment properties of order statistics or spacing.