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.

Unconditional Maximum Likelihood Estimation of Linear and Log-Linear Dynamic Models for Spatial Panels

Abstract: This article hammers out the estimation of a fixed effects dynamic panel data model extended to include either spatial error autocorrelation or a spatially lagged dependent variable. To overcome the inconsistencies associated with the traditional least-squares dummy estimator, the models are first-differenced to eliminate the fixed effects and then the unconditional likelihood function is derived taking into account the density function of the first-differenced observations on each spatial unit. When exogenous variables are omitted, the exact likelihood function is found to exist. When exogenous variables are included, the pre-sample values of these variables and thus the likelihood function must be approximated. Two leading cases are considered: the Bhargava and Sargan approximation and the Nerlove and Balestra approximation. As an application, a dynamic demand model for cigarettes is estimated based on panel data from 46 U.S. states over the period from 1963 to 1992.

Capacity-constrained point distributions: a variant of Lloyd's method

Abstract: We present a new general-purpose method for optimizing existing point sets. The resulting distributions possess high-quality blue noise characteristics and adapt precisely to given density functions. Our method is similar to the commonly used Lloyd's method while avoiding its drawbacks. We achieve our results by utilizing the concept of capacity, which for each point is determined by the area of its Voronoi region weighted with an underlying density function. We demand that each point has the same capacity. In combination with a dedicated optimization algorithm, this capacity constraint enforces that each point obtains equal importance in the distribution. Our method can be used as a drop-in replacement for Lloyd's method, and combines enhancement of blue noise characteristics and density function adaptation in one operation.

One-Class Classification by Combining Density and Class Probability Estimation

Abstract: One-class classification has important applications such as outlier and novelty detection. It is commonly tackled using density estimation techniques or by adapting a standard classification algorithm to the problem of carving out a decision boundary that describes the location of the target data. In this paper we investigate a simple method for one-class classification that combines the application of a density estimator, used to form a reference distribution, with the induction of a standard model for class probability estimation. In this method, the reference distribution is used to generate artificial data that is employed to form a second, artificial class. In conjunction with the target class, this artificial class is the basis for a standard two-class learning problem. We explain how the density function of the reference distribution can be combined with the class probability estimates obtained in this way to form an adjusted estimate of the density function of the target class. Using UCI datasets, and data from a typist recognition problem, we show that the combined model, consisting of both a density estimator and a class probability estimator, can improve on using either component technique alone when used for one-class classification. We also compare the method to one-class classification using support vector machines.

Local distributions and rate fluctuations in a unified scaling law for earthquakes.

Abstract: A recently proposed unified scaling law for interoccurrence times of earthquakes is analyzed, both theoretically and with data from Southern California We decompose the corresponding probability density into local-instantaneous distributions, which scale with the rate of earthquake occurrence The fluctuations of the rate, characterizing the nonstationarity of the process, show a double power-law distribution and are fundamental to determine the overall behavior, described by a double power law as well