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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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Journal ArticleDOI
TL;DR: For this mixed RF-FSO cooperative system, novel closed-form mathematical expressions are derived for cumulative distribution function, probability density function and moment generating function of the equivalent signal-to-noise ratio in terms of Meijer-G function.
Abstract: In this study, the error performance and the capacity analysis is performed for the decode-and-forward based dual-hop asymmetric radio frequency-free space optical communication (RF-FSO) system. The RF link is characterised by Nakagami- m fading and the FSO link is characterised by path loss, Gamma-Gamma distributed turbulence and pointing error. For this mixed RF-FSO cooperative system, novel closed-form mathematical expressions are derived for cumulative distribution function, probability density function and moment generating function of the equivalent signal-to-noise ratio in terms of Meijer-G function. Using these channel statistics, new finite power series based analytical expressions are obtained for the outage probability, the average bit error rate for various binary and M -ary modulation techniques and the average channel capacity of the considered system in terms of Meijer-G function. As a special case, the analytical framework can also be obtained for channel statistics and performance metrics of dual-hop mixed Rayleigh-Gamma-Gamma system. Simulation results validate the proposed mathematical analysis. The effects of fading, turbulence and pointing error are studied on the outage probability, average bit error rate and channel capacity of the asymmetric RF-FSO system.

95 citations

Journal ArticleDOI
TL;DR: In this paper, the full probability density function (PDF) of inflationary curvature perturbations was calculated, even in the presence of large quantum backreaction, using the stochastic-$\delta N$ formalism.
Abstract: We calculate the full probability density function (PDF) of inflationary curvature perturbations, even in the presence of large quantum backreaction. Making use of the stochastic-$\delta N$ formalism, two complementary methods are developed, one based on solving an ordinary differential equation for the characteristic function of the PDF, and the other based on solving a heat equation for the PDF directly. In the classical limit where quantum diffusion is small, we develop an expansion scheme that not only recovers the standard Gaussian PDF at leading order, but also allows us to calculate the first non-Gaussian corrections to the usual result. In the opposite limit where quantum diffusion is large, we find that the PDF is given by an elliptic theta function, which is fully characterised by the ratio between the squared width and height (in Planck mass units) of the region where stochastic effects dominate. We then apply these results to the calculation of the mass fraction of primordial black holes from inflation, and show that no more than $\sim 1$ $e$-fold can be spent in regions of the potential dominated by quantum diffusion. We explain how this requirement constrains inflationary potentials with two examples.

95 citations

Journal ArticleDOI
Jacques de Guenin1
TL;DR: In this paper a method is provided for solving the problem in the general case, where no assumption is made concerning the form of the detection probability function, and a theorem is derived that gives a general relation governing the optimal solution.
Abstract: The fundamental problem of search theory is to allocate a given amount of search effort in such a way as to maximize the over-all probability of discovering an object located in a given space. The problem has already been solved under the assumption that the probability of detecting the object is a negative exponential function of the search effort density, this assumption seems to be fairly realistic in many military applications, but has definite drawbacks in others. In this paper a method is provided for solving the problem in the general case, where no assumption is made concerning the form of the detection probability function. A theorem is derived that gives a general relation governing the optimal solution.

95 citations

Proceedings ArticleDOI
29 Jun 2009
TL;DR: This paper presents various indexing schemes with linear or near-linear space and logarithmic query time, and extends to the external memory model in which the goal is to minimize the number of disk accesses when querying the index.
Abstract: Querying uncertain data has emerged as an important problem in data management due to the imprecise nature of many measurement data. In this paper we study answering range queries over uncertain data. Specifically, we are given a collection P of n points in R, each represented by its one-dimensional probability density function (pdf). The goal is to build an index on P such that given a query interval I and a probability threshold τ, we can quickly report all points of P that lie in I with probability at least τ. We present various indexing schemes with linear or near-linear space and logarithmic query time. Our schemes support pdf's that are either histograms or more complex ones such as Gaussian or piecewise algebraic. They also extend to the external memory model in which the goal is to minimize the number of disk accesses when querying the index.

95 citations

Journal ArticleDOI
TL;DR: Simulation results on test video sequences show an improved performance both in terms of the peak signal-to-noise ratio and the perceptual quality compared to that of the other denoising algorithms.
Abstract: The paper proposes a joint probability density function to model the video wavelet coefficients of any two neighboring frames and then applies this statistical model for denoising. The parameter of the density function that measures the correlation between the wavelet coefficients of the two frames is used as an index for the motion. The joint density function is employed for spatial filtering of the noisy wavelet coefficients by developing a bivariate maximum a posteriori estimator. A recursive time averaging of the spatially filtered wavelet coefficients is adopted for further noise reduction. Simulation results on test video sequences show an improved performance both in terms of the peak signal-to-noise ratio and the perceptual quality compared to that of the other denoising algorithms

95 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023382
2022906
2021906
20201,047
20191,117
20181,083