Showing papers on "Natural exponential family published in 1986"
TL;DR: In this article, a new three-parameter family of distributions on the positive numbers is proposed, which includes the stable distributions, the gamma, the degenerate and the inverse Gaussian distributions.
Abstract: SUMMARY A new three-parameter family of distributions on the positive numbers is proposed. It includes the stable distributions on the positive numbers, the gamma, the degenerate and the inverse Gaussian distributions. The family is characterized by the Laplace transform, from which moments, convolutions, infinite divisibility, unimodality and other properties are derived. The density is complicated, but a simple saddlepoint approximation is provided. Weibull and Gompertz distributions are naturally mixed over some of the distributions. The family is natural exponential in one of the parameters. The distributions are relevant for application as frailty distributions in life table methods for heterogeneous populations. Desirable properties of such distributions are discussed. As an example survival after myocardial infarction is considered.
687 citations
TL;DR: In this article, the authors derived point and interval estimates, as well as tests of hypotheses, for the parameters of two-parameter exponential distribution, based on the results of a hybrid life test for the cases of sampling with and without replacement.
36 citations
TL;DR: In this paper, the principle of obtaining a measure of dependence based on the notion of information gain is examined for normal models and for several bivariate exponential models, and it is shown that, under normal models, the principle usually gives good measures.
Abstract: SUMMARY The principle of obtaining a measure of dependence based on the notion of information gain is examined for normal models and for several bivariate exponential models. It is shown that, under normal models, the principle usually gives good measures. It is also shown that it gives interesting measures for some exponential models.
12 citations
TL;DR: In this article, the problem of determining whether a given setP of mutually equivalent probability distributions constitutes an exponential family was discussed, and it was shown that many familiar classes of distributions (e.g., Cauchy-,tn-, logistic-) are not exponential families.
Abstract: The problem discussed is whether a given setP of mutually equivalent probability distributions constitutes an exponential family or not. As an alternative to the well known characterization by linear independence an analytic method is pointed out which allows one to demonstrate in a relatively easy way that many familiar classes of distributions (e.g. Cauchy-,t
n-, logistic-) are not exponential families.
11 citations
TL;DR: In this paper, it was shown that the rate of exponential convergence for the maximum likelihood estimator attains the Bahadur bound if and only if the underlying distribution is a member of the exponential family of distributions.
7 citations
TL;DR: In this paper, the locally uniformly most powerful unbiased Lagrange multiplier test of normality of regression disturbances within the family of power exponential distributions was developed and compared in a Monte Carlo study with 6 well-known tests across 12 alternative nonnormal distributions.
Abstract: This article develops the locally uniformly most powerful unbiased Lagrange multiplier test of normality of regression disturbances within the family of power exponential distributions. The small sample power properties of the test are compared in a Monte Carlo study with 6 well-known tests across 12 alternative nonnormal distributions. In addition, the finite sample power properties for nonnormal alternatives within the power exponential family are summarized by estimating response surfaces. The results suggest that the proposed text is computationally convenient and possesses relatively attractive power properties even against alternatives outside the power exponential family.
6 citations
3 citations
TL;DR: The null distribution of the likelihood ratio criterion for testing the quality of scale parameters of p(p>2) two parameter exponential distributions for the case of equal sample sizes is obtained in a closed form for the first time as discussed by the authors.
Abstract: In this paper, null distribution of the likelihood ratio criterion for testing the quality of scale parameters of p(p>2) two parameter exponential distributions for the case of equal sample sizes is obtained in a closed form for the first time. A short table of the critical values of the test statistic is also presented.
3 citations
2 citations
TL;DR: Systematic and simple characterizations are presented for several familiar distributions in exponential family by means of the principle of minimum cross-entropy (minimum discrimination information).
Abstract: Systematic and simple characterizations are presented for several familiar distributions in exponential family by means of the principle of minimum cross-entropy (minimum discrimination information). The suitable prior distributions and the appropriate constraints on expected values are given for the underlying distributions.
TL;DR: In this article, decision theory is applied to determine minimax policies of simultaneous control and estimation for stochastic system (1), where the binomial distribution with unknown parameter and the class of prior distributions of parameter is restricted by fixing the second moment.
Abstract: In the present paper methods of the decision theory are applied to determine minimax policies of simultaneous control and estimation for stochastic system (1). There are solved the following cases: a)when disturbances of the system have the binomial distribution with unknown parameter b)when disturbances of the system have distribution belonging to an exponential family dependent on natural unknown parameter and the class of prior distributions of parameter is restricted by fixing the second moment In both cases open analytical forms of minimax policies are given
01 Oct 1986
TL;DR: In this article, several methods for confidence set estimation of a change-point in a sequence of independent observations from completely specified distributions are discussed, and the method based on the likelihood ratio statistic is extended to the case of observations from a one-parameter exponential family.
Abstract: : Several methods are discussed for confidence set estimation of a change-point in a sequence of independent observations from completely specified distributions. The method based on the likelihood ratio statistic is extended to the case of independent observations from a one parameter exponential family. Joint confidence sets for the change-point and the parameters of the exponential family are also considered.
TL;DR: In this article, it is shown that one can construct set-compound estimators £ such that t ̂ times its risk less a minimum Bayes risk converges to zero with a rate as t -*•• •> provided that the components of θ are in a compact set and 2 ~ 2 matrix = σ I with σ unknown under squared error loss.
Abstract: Abstract. This paper is concerned with the problem of the estimation of the mean £ of a t variate normal distribution with covariance 2 ~ 2 matrix = σ I with σ unknown under squared error loss. It is shown that one can construct set-compound estimators £ such that t ̂ times its risk less a minimum Bayes risk converges to zero with a rate as t -*• •> provided that the components of θ are in a compact set and 2 ~