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.
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TL;DR: In this paper, two approaches to characterize transport by groundwater are compared: the common one in which solute movement is represented in terms of concentration as function of space and time and that of a travel-time probability distribution function (p.d.), defined as the probability of crossing a compliance surface by a solute particle.
107 citations
29 Sep 1999
TL;DR: It is shown that, if the probability density function of vectors that arise from random, unwatermarked media is a zero-mean, spherical Gaussian, then the probability that such a detector will give a false detection is given exactly by a simple ratio of two definite integrals.
Abstract: Several methods of watermark detection involve computing a vector from some input media, computing the normalized correlation between that vector and a predefined watermark vector, and comparing the result against a threshold. We show that, if the probability density function of vectors that arise from random, unwatermarked media is a zero-mean, spherical Gaussian, then the probability that such a detector will give a false detection is given exactly by a simple ratio of two definite integrals. This expression depends only on the detection threshold and the dimensionality of the watermark vector.
106 citations
TL;DR: A unique parabolic relation is observed to link skewness and kurtosis of around ten thousand density fluctuation signals, measured over the whole cross section of a toroidal magnetized plasma for a broad range of experimental conditions.
Abstract: A unique parabolic relation is observed to link skewness and kurtosis of around ten thousand density fluctuation signals, measured over the whole cross section of a toroidal magnetized plasma for a broad range of experimental conditions. All the probability density functions of the measured signals, including those characterized by a negative skewness, are universally described by a special case of the Beta distribution. Fluctuations in the drift-interchange frequency range are necessary and sufficient to assure that probability density functions can be described by this specific Beta distribution.
106 citations
TL;DR: In this article, the authors report measurements of the spreading rate of pairs of tracer particles in an intensely turbulent laboratory water flow and compare their measurements of this turbulent relative dispersion with the longstanding work of Richardson and Batchelor.
Abstract: We report measurements of the spreading rate of pairs of tracer particles in an intensely turbulent laboratory water flow. We compare our measurements of this turbulent relative dispersion with the longstanding work of Richardson and Batchelor, and find excellent agreement with Batchelor's predictions. The distance neighbour function, the probability density function of the relative dispersion, is measured and compared with existing models. We also investigate the recently proposed exit time analysis of relative dispersion.
106 citations
TL;DR: The results demonstrate that the image quality of the method presented is comparable to that of an established model-based strategy when optimization of the model parameter is carried out and yields superior results to non-optimized model parameters.
Abstract: Variable density random sampling patterns have recently become increasingly popular for accelerated imaging strategies, as they lead to incoherent aliasing artifacts. However, the design of these sampling patterns is still an open problem. Current strategies use model assumptions like polynomials of different order to generate a probability density function that is then used to generate the sampling pattern. This approach relies on the optimization of design parameters which is very time consuming and therefore impractical for daily clinical use. This work presents a new approach that generates sampling patterns by making use of power spectra of existing reference data sets and hence requires neither parameter tuning nor an a priori mathematical model of the density of sampling points. The approach is validated with downsampling experiments, as well as with accelerated in vivo measurements. The proposed approach is compared with established sampling patterns, and the generalization potential is tested by using a range of reference images. Quantitative evaluation is performed for the downsampling experiments using RMS differences to the original, fully sampled data set. Our results demonstrate that the image quality of the method presented in this paper is comparable to that of an established model-based strategy when optimization of the model parameter is carried out and yields superior results to non-optimized model parameters. However, no random sampling pattern showed superior performance when compared to conventional Cartesian subsampling for the considered reconstruction strategy.
106 citations