Probability density function

About: Probability density function is a research topic. Over the lifetime, 22321 publications have been published within this topic receiving 422885 citations. The topic is also known as: probability function & PDF.

The General Theory of Random Choices in Relation to the Invariant Cardinal Utility Function and the Specific Probability Function. The (U, θ) Model A General Overview

Abstract: Allais’ general theory of random choices is essentially based on the consideration of the invariant cardinal utility function and the whole distribution of cardinal utilities, and on the general preference for security in the neighbourhood of certainty when large sums are at stake.

Exponentiated Weibull distribution family under aperture averaging for Gaussian beam waves

Abstract: Nowadays, the search for a distribution capable of modeling the probability density function (PDF) of irradiance data under all conditions of atmospheric turbulence in the presence of aperture averaging still continues. Here, a family of PDFs alternative to the widely accepted Log-Normal and Gamma-Gamma distributions is proposed to model the PDF of the received optical power in free-space optical communications, namely, the Weibull and the exponentiated Weibull (EW) distribution. Particularly, it is shown how the proposed EW distribution offers an excellent fit to simulation and experimental data under all aperture averaging conditions, under weak and moderate turbulence conditions, as well as for point-like apertures. Another very attractive property of these distributions is the simple closed form expression of their respective PDF and cumulative distribution function.

A non-parametric and scale-independent method for cluster analysis – I. The univariate case

Abstract: The detection and analysis of structure and substructure in systems of galaxies is a well-known problem. Several methods of analysis exist with different ranges of applicability and giving different results. The aim of the present paper is to describe a general procedure of wide applicability that is based on a minimum number of general assumptions and gives an objective, testable, scale-independent and non-parametric estimate of the clustering pattern of a sample of observational data. The method follows the idea that the presence of a cluster in a data sample is indicated by a peak in the probability density underlying the data. There are two steps: the first is estimation of the probability density and the second is identification of the clusters

Protein distance constraints predicted by neural networks and probability density functions.

Abstract: We predict interatomic Calpha distances by two independent data driven methods. The first method uses statistically derived probability distributions of the pairwise distance between two amino acids, whilst the latter method consists of a neural network prediction approach equipped with windows taking the context of the two residues into account. These two methods are used to predict whether distances in independent test sets were above or below given thresholds. We investigate which distance thresholds produce the most information-rich constraints and, in turn, the optimal performance of the two methods. The predictions are based on a data set derived using a new threshold which defines when sequence similarity implies structural similarity. We show that distances in proteins are predicted more accurately by neural networks than by probability density functions. We show that the accuracy of the predictions can be further increased by using sequence profiles. A threading method based on the predicted distances is presented. A homepage with software, predictions and data related to this paper is available at http://www.cbs.dtu.dk/services/CPHmodels/.

The continuous ranked probability score for circular variables and its application to mesoscale forecast ensemble verification

Abstract: An analogue of the linear continuous ranked probability score is introduced that applies to probabilistic forecasts of circular quantities. This scoring rule is proper and thereby discourages hedging. The circular continuous ranked probability score reduces to angular distance when the forecast is deterministic, just as the linear continuous ranked probability score generalizes the absolute error. Furthermore, the continuous ranked probability score provides a direct way of comparing deterministic forecasts, discrete forecast ensembles, and post-processed forecast ensembles that can take the form of probability density functions. The circular continuous ranked probability score is used in this study to assess predictions of 10 m wind direction for 361 cases of mesoscale, short-range ensemble forecasts over the North American Pacic Northwest. Reference probability forecasts based on the ensemble mean and its forecast error history over the period outperform probability forecasts constructed directly from the ensemble sample statistics. These results suggest that short-term forecast uncertainty is not yet well predicted at mesoscale resolutions near the surface, despite the inclusion of multi-scheme physics diversity and surface boundary parameter perturbations in the mesoscale ensemble design. 1