Topic
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.
Papers published on a yearly basis
Papers
More filters
TL;DR: A method for defining a probability density function over a set of Luminaires is presented that allows the direct lighting calculation to be carried out with a number of sample points that is independent of the number of luminaires.
Abstract: In a distributed ray tracer, the sampling strategy is the crucial part of the direct lighting calculation. Monte Carlo integration with importance sampling is used to carry out this calculation. Importance sampling involves the design of integrand-specific probability density functions that are used to generate sample points for the numerical quadrature. Probability density functions are presented that aid in the direct lighting calculation from luminaires of various simple shapes. A method for defining a probability density function over a set of luminaires is presented that allows the direct lighting calculation to be carried out with a number of sample points that is independent of the number of luminaires.
251 citations
TL;DR: In this article, the effect of roughness of surfaces of a slider bearing on the load-carrying capacity and friction force was studied, and the distinction between waviness and roughness was made between random quantities which may be characterized by a probability density function, determined experimentally.
Abstract: The effect of roughness of surfaces of a slider bearing on the load-carrying capacity and friction force, is studied. The distinction is made between waviness and roughness, the latter being treated as a random quantity which may be characterized by a probability density function, determined experimentally. Results can be obtained in closed form suitable for calculation if a Beta distribution is assumed. Actually, this can approximate quite closely a Gaussian distribution, yielding quite accurate results. However, the procedure developed can be carried out for any desired distribution.
251 citations
Abstract: A new stochastic model for the motion of particle pairs in isotropic high-Reynolds-number turbulence is proposed. The model is three-dimensional and its formulation takes account of recent improvements in the understanding of one-particle models. In particular the model is designed so that if the particle pairs are initially well mixed in the fluid, they will remain so. In contrast to previous models, the new model leads to a prediction for the particle separation probability density function which is in qualitative agreement with inertial subrange theory. The values of concentration variance from the model show encouraging agreement with experimental data. The model results suggest that, at large times, the intensity of concentration fluctuations (i.e. standard deviation of concentration divided by mean concentration) tends to zero in stationary conditions and to a constant in decaying turbulence.
250 citations
TL;DR: In this paper, the authors review the three available methods for modeling drop size distributions: the maximum entropy method, the discrete probability function method, and the empirical method and compare them with the empirical estimation of drop diameter.
250 citations
TL;DR: It is sufficient to find the orthonormal rotation y=Wz of prewhitened sources z=Vx, which minimizes the mean squared error of the reconstruction of z from the rectified version y/sup +/ of y, which shows in particular the fast convergence of the rotation and geodesic methods.
Abstract: We consider the task of solving the independent component analysis (ICA) problem x=As given observations x, with a constraint of nonnegativity of the source random vector s. We refer to this as nonnegative independent component analysis and we consider methods for solving this task. For independent sources with nonzero probability density function (pdf) p(s) down to s=0 it is sufficient to find the orthonormal rotation y=Wz of prewhitened sources z=Vx, which minimizes the mean squared error of the reconstruction of z from the rectified version y/sup +/ of y. We suggest some algorithms which perform this, both based on a nonlinear principal component analysis (PCA) approach and on a geodesic search method driven by differential geometry considerations. We demonstrate the operation of these algorithms on an image separation problem, which shows in particular the fast convergence of the rotation and geodesic methods and apply the approach to a musical audio analysis task.
249 citations