Search results for "Natural exponential family"
showing 4 items of 4 documents
A Software Tool for the Exponential Power Distribution: The normalp Package
2005
In this paper we present the normalp package, a package for the statistical environment R that has a set of tools for dealing with the exponential power distribution. In this package there are functions to compute the density function, the distribution function and the quantiles from an exponential power distribution and to generate pseudo-random numbers from the same distribution. Moreover, methods concerning the estimation of the distribution parameters are described and implemented. It is also possible to estimate linear regression models when we assume the random errors distributed according to an exponential power distribution. A set of functions is designed to perform simulation studi…
Maximum probability estimators in the case of exponential distribution
1975
In 1966–1969L. Weiss andJ. Wolfowitz developed the theory of „maximum probability” estimators (m.p.e.'s). M.p.e.'s have the property of minimizing the limiting value of the risk (see (2.10).) In the present paper, therfore, after a short description of the new method, a fundamental loss function is introduced, for which—in the so-called regular case—the optimality property of the maximum probability estimators yields the classical result ofR.A. Fisher on the asymptotic efficiency of the maximum likelihood estimator. Thereby it turns out that the m.p.e.'s possess still another important optimality property for this loss function. For the latter the parameters of the exponential distribution—…
Some Remarks on Exponential Families
1987
Abstract The following facts may serve to provide a feeling about how restrictive the assumption of an exponential family is. (a) A one-parameter exponential family in standard form with respect to Lebesgue measure is a location parameter family iff it is normal with fixed variance. (b) It is a scale parameter family iff it is gamma with fixed shape parameter. Both facts are known (see Borges and Pfanzagl 1965; Ferguson 1962; Lindley 1958) but may not have received as much attention as they deserve. Under the assumption of differentiable densities, short and elementary proofs are given.
On achieving near-optimal “Anti-Bayesian” Order Statistics-Based classification fora asymmetric exponential distributions
2013
Published version of a Chapter in the book: Computer Analysis of Images and Patterns. Also available from the publisher at: http://dx.doi.org/10.1007/978-3-642-40261-6_44 This paper considers the use of Order Statistics (OS) in the theory of Pattern Recognition (PR). The pioneering work on using OS for classification was presented in [1] for the Uniform distribution, where it was shown that optimal PR can be achieved in a counter-intuitive manner, diametrically opposed to the Bayesian paradigm, i.e., by comparing the testing sample to a few samples distant from the mean - which is distinct from the optimal Bayesian paradigm. In [2], we showed that the results could be extended for a few sym…