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.

Stochastic reconstruction of sandstones

Abstract: A simulated annealing algorithm is employed to generate a stochastic model for a Berea sandstone and a Fontainebleau sandstone, with each a prescribed two-point probability function, lineal-path function, and ''pore size'' distribution function, respectively. We find that the temperature decrease of the annealing has to be rather quick to yield isotropic and percolating configurations. A comparison of simple morphological quantities indicates good agreement between the reconstructions and the original sandstones. Also, the mean survival time of a random walker in the pore space is reproduced with good accuracy. However, a more detailed investigation by means of local porosity theory shows that there may be significant differences of the geometrical connectivity between the reconstructed and the experimental samples. (c) 2000 The American Physical Society.

A Complex Generalized Gaussian Distribution— Characterization, Generation, and Estimation

Abstract: The generalized Gaussian distribution (GGD) provides a flexible and suitable tool for data modeling and simulation, however the characterization of the complex-valued GGD, in particular generation of samples from a complex GGD have not been well defined in the literature. In this correspondence, we provide a thorough presentation of the complex-valued GGD by: (i) constructing the probability density function (pdf); (ii) defining a procedure for generating random numbers from the complex-valued GGD; and (iii) implementing a maximum likelihood estimation (MLE) procedure for the shape and covariance parameters in the complex domain. We quantify the performance of the MLE with simulations and actual radar data.

On Some Global Measures of the Deviations of Density Function Estimates

Abstract: We consider density estimates of the usual type generated by a weight function. Limt theorems are obtained for the maximum of the normalized deviation of the estimate from its expected value, and for quadratic norms of the same quantity. Using these results we study the behavior of tests of goodness-of-fit and confidence regions based on these statistics. In particular, we obtain a procedure which uniformly improves the chi-square goodness-of-fit test when the number of observations and cells is large and yet remains insensitive to the estimation of nuisance parameters. A new limit theorem for the maximum absolute value of a type of nonstationary Gaussian process is also proved.

A neural network approach to statistical pattern classification by 'semiparametric' estimation of probability density functions

Abstract: A method for designing near-optimal nonlinear classifiers, based on a self-organizing technique for estimating probability density functions when only weak assumptions are made about the densities, is described. The method avoids disadvantages of other existing methods by parametrizing a set of component densities from which the actual densities are constructed. The parameters of the component densities are optimized by a self-organizing algorithm, reducing to a minimum the labeling of design samples. All the required computations are realized with the simple sum-of-product units commonly used in connectionist models. The density approximations produced by the method are illustrated in two dimensions for a multispectral image classification task. The practical use of the method is illustrated by a small speech recognition problem. Related issues of invariant projections, cross-class pooling of data, and subspace partitioning are discussed. >

Probabilistic analysis of power flows

Abstract: The paper describes and examines a technique which permits the power-flow problem in a power system to be analysed probabilistically instead of using normal deterministic methods. All the nodal loads and generation are defined as random variables and the power flow in each line is computed in terms of a probability density function. The expected values and standard deviation of each power flow are also calculated, and, in addition, the overall balance of power in the system is determined in terms of a density function. The purpose of this analysis is to account for the errors and statistical variations known to exist in the operation and planning of systems within one solution. This enables the power-flow problem to be treated objectively and allows quantitative assessment of reliability and security. The paper compares the results obtained probabilistically with those that would be obtained deterministically, and shows the much wider range of information gained in this type of analysis.