Showing papers on "K-distribution published in 1976"

Approximate Posterior Distributions

Abstract: This paper proposes the use of approximate posterior distributions resulting from operational prior distributions chosen with regard to the realized likelihood function. L.J. Savage's “precise measurement” is generalized for approximation in terms of an arbitrary operational prior density, including mixed-type prior distributions with positive probabilities on singular subsets. A new approximation is also given relating such distributions to absolutely continuous distributions with high local concentrations of density. Mixed-type distributions constructed from the natural conjugate prior distributions are proposed and illustrated in the normal-sampling case for unified Bayesian inference in testing and estimation contexts.

A Two-Dimensional Continuum of a Priori Probability Distributions on Constituents

Abstract: Hintikka has defined a one-dimensional continuum of a priori probability distributions on constituents and has built on it a two-dimensional continuum of inductive methods with the aid of Carnap’s λ-continuum ([1]), which plays also a fundamental role in his continuum of a priori distributions, and the formula of Bayes ([2]). Here a two-dimensional continuum of a priori probability distributions will be introduced. On its base a three-dimensional continuum of inductive methods can be constructed in the same way as Hintikka has done. The importance of the new continuum of a priori distributions, which is also based on Carnap’s λ-continuum but in a completely different way, is that it leaves room for almost all kinds of a priori considerations, whereas Hintikka’s continuum admits only considerations that lead to increasing probability for the constituents by increasing size.

Optimum detection and signal design for v.l.f. channels

Abstract: A new generalized model for atmospheric radio noise is briefly described and justified by comparison with observed probability distributions. A special case of this generalized model is then compared to the observed noise statistics at the very low frequency end of the spectrum. This model is then applied to the detection of known signals in in the presence of noise to determine the optimal receiver structure. The performance of the detector, specified by the upper bound on the probability of error, is assessed and is seen to depend on the signal shape, the time-bandwidth product, and signal-to-noise ratio. The optimal signal to minimize the probability of error is then determined.

Two characteristic properties of normal distributions in the class NH

Abstract: In this note are deduced two characterizations of normal distributions in the class NH of probability distributions on a plane whose densities admit diagonal expansions in series of Hermite polynomials and the marginal distributions are standardized and normal.