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.

Blind image quality assessment through anisotropy

Abstract: We describe an innovative methodology for determining the quality of digital images. The method is based on measuring the variance of the expected entropy of a given image upon a set of predefined directions. Entropy can be calculated on a local basis by using a spatial/spatial-frequency distribution as an approximation for a probability density function. The generalized Renyi entropy and the normalized pseudo-Wigner distribution (PWD) have been selected for this purpose. As a consequence, a pixel-by-pixel entropy value can be calculated, and therefore entropy histograms can be generated as well. The variance of the expected entropy is measured as a function of the directionality, and it has been taken as an anisotropy indicator. For this purpose, directional selectivity can be attained by using an oriented 1-D PWD implementation. Our main purpose is to show how such an anisotropy measure can be used as a metric to assess both the fidelity and quality of images. Experimental results show that an index such as this presents some desirable features that resemble those from an ideal image quality function, constituting a suitable quality index for natural images. Namely, in-focus, noise-free natural images have shown a maximum of this metric in comparison with other degraded, blurred, or noisy versions. This result provides a way of identifying in-focus, noise-free images from other degraded versions, allowing an automatic and nonreference classification of images according to their relative quality. It is also shown that the new measure is well correlated with classical reference metrics such as the peak signal-to-noise ratio.

Performance Analysis of MIMO-MRC in Double-Correlated Rayleigh Environments

Abstract: We consider multiple-input multiple-output (MIMO) transmit beamforming systems with maximum ratio combining (MRC) receivers The operating environment is Rayleigh fading with both transmit and receive spatial correlation We present exact expressions for the probability density function (pdf) of the output signal-to-noise ratio, as well as the system outage probability The results are based on explicit closed-form expressions which we derive for the pdf and cumulative distribution function of the maximum eigenvalue of double-correlated complex Wishart matrices For systems with two antennas at either the transmitter or the receiver, we also derive exact closed-form expressions for the symbol-error rate The new expressions are used to prove that MIMO-MRC achieves the maximum available spatial diversity order, and to demonstrate the effect of spatial correlation The analysis is validated through comparison with Monte Carlo simulations

Estimating the probability of failure when testing reveals no failures

Abstract: Formulas for estimating the probability of failure when testing reveals no errors are introduced. These formulas incorporate random testing results, information about the input distribution; and prior assumptions about the probability of failure of the software. The formulas are not restricted to equally likely input distributions, and the probability of failure estimate can be adjusted when assumptions about the input distribution change. The formulas are based on a discrete sample space statistical model of software and include Bayesian prior assumptions. Reusable software and software in life-critical applications are particularly appropriate candidates for this type of analysis. >

Digital Generation of Non‐Gaussian Stochastic Fields

Abstract: A method by which sample fields of a multidimensional non‐Gaussian homogeneous stochastic field can be generated is developed. The method first generates Gaussian sample fields and then maps them into non‐Gaussian sample fields with the aid of an iterative procedure. Numerical examples indicate that the procedure is very efficient and generated sample fields satisfy the target spectral density and probability distribution function accurately. The proposed method has a wide range of applicability to engineering problems involving stochastic fields where the Gaussian assumption is not appropriate.

On the Origin of the Global Schmidt Law of Star Formation

Abstract: One of the most puzzling properties of observed galaxies is the universality of the empirical correlation between the star formation rate and the average gas surface density on kiloparsec scales (the Schmidt law). In this study, I present results of self-consistent cosmological simulations of high-redshift galaxy formation that reproduce the Schmidt law naturally, without assuming it, and provide some clues to this puzzle. The simulations have a dynamic range high enough to identify individual star-forming regions. The results indicate that the global Schmidt law is a manifestation of the overall density distribution of the interstellar medium. In particular, the density probability distribution function (PDF) in the simulated disks has a well-defined generic shape that can be approximated by a lognormal distribution at high densities. The PDF in a given region of the disk depends on the local average surface density Σg. The dependence is such that the fraction of gas mass in the high-density tail of the distribution scales as Σ with n ≈ 1.4, which gives rise to the Schmidt-like correlation. The high-density tail of the PDF is remarkably insensitive to the inclusion of feedback and details of the cooling and heating processes. This indicates that the global star formation rate is determined by the supersonic turbulence driven by gravitational instabilities on large scales, rather than stellar feedback or thermal instabilities on small scales.