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About 10,000 papers for “Probability density function”

On system failure probability density function

Campioni, Luca, Vestrucci, Paolo · RePEc: Research Papers in Economics

The assessment of the system unreliability is usually accomplished through well-known tools such as block diagram, fault tree, Monte Carlo and others. These methods imply the knowledge of the failure probability density function of each component “k†(pdf pk). For this reason, possibly, the system failure probability density function (psys) has never been explicitly derived.

Cited by 0

Probability density function of amplitude scintillations

G. Ortgies · Electronics Letters · 1985

The letter reports on amplitude scintillation measurements of the orbital test satellite (OTS) BO carrier beacon carried out from June to December 1983. The scintillations are here characterised by standard deviations of the amplitude fluctuations and by the distribution of amplitude deviations from their mean. It is known that during scintillations log-amplitudes are normally distributed for short time intervals (1 min). The long-term probability density of amplitude scintillations can be calculated using recorded 1 mm standard deviations σ. The probability density function of log ((σ−σN)/dB) can be well approximated by a Gaussian distribution, where σN is the 1 min standard deviation due to thermal noise alone.

Cited by 19

Probability density for SURD scoring function.

Jenny Farmer (5211116), Donald Jacobs (4049143) · Figshare · 2018

<p>The probability density for the log-likelihood score based on single order statistics for different sample sizes exhibits near sample size invariance. The solid black line is a consensus of all sample sizes combined, and the dashed lines show example levels of SURD coverage.</p>

Cited by 0Open access

Cumulative probability and probability density function of extinction event.

Lanxin Zhang (11874204), Junyu Wang (2409904), Max von Kleist (152808) · Figshare · 2021

<p><i>N</i> = 1000 virtual patients were sampled from the pharmacokinetic parameter distributions defined in Table 2 of [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1009295#pcbi.1009295.ref011" target="_blank">11</a>]. 50 mg dose of DTG / day was ingested for three days, first dose was taken at <i>t</i><sub>0</sub> = 0, coinciding with viral exposure. <b>A</b>. Cumulative extinction probability for one initial virus. <b>B</b>. Probability density function of extinction for one initial virus. <b>C</b>. Cumulative extinction probability for 20 initial viruses. <b>D</b>. Probability density function of extinction for 20 initial viruses. The red and green lines depict the respective median values, whereas the dark- and light grey areas present the quartile range and 2.5%–97.5% confidence range, taking inter-individual pharmacokinetic differences into account.</p>

Cited by 0Open access

The Column Density Probability Density Function of Cygnus-X

Yuchen Xing, Keping Qiu · ArXiv.org · 2026

The density distribution within molecular clouds offers critical insights into their underlying physical processes, which are essential for understanding star formation. As a statistical measure of column density on the cloud scale, the shape and evolution of the column density probability density function (N-PDF) serve as important tools for understanding the dynamics between turbulence and gravity. Here we investigate the N-PDFs of Cygnus-X using the column density map obtained from Herschel, supplemented by HI and Young Stellar Objects (YSO) data. We find that the N-PDFs of Cygnus-X and four sub-regions display log-normal + power-law shapes, indicating the combined effects of turbulence and gravity in sculpting the density structure. We find evidence that the power-law segment of the N-PDFs flattens over time, and the transitional column density can be seen as a unique and stable star formation threshold specific to each molecular cloud. These results not only clarify the physical state of Cygnus-X but also emphasize the utility of the N-PDF as a statistical diagnostic tool, as it is an accessible indicator of evolutionary stages and star formation thresholds in molecular clouds.

Cited by 0Open access

The Column Density Probability Density Function of Cygnus-X

Yuchen Xing, Keping Qiu · arXiv (Cornell University) · 2026

The density distribution within molecular clouds offers critical insights into their underlying physical processes, which are essential for understanding star formation. As a statistical measure of column density on the cloud scale, the shape and evolution of the column density probability density function (N-PDF) serve as important tools for understanding the dynamics between turbulence and gravity. Here we investigate the N-PDFs of Cygnus-X using the column density map obtained from Herschel, supplemented by HI and Young Stellar Objects (YSO) data. We find that the N-PDFs of Cygnus-X and four sub-regions display log-normal + power-law shapes, indicating the combined effects of turbulence and gravity in sculpting the density structure. We find evidence that the power-law segment of the N-PDFs flattens over time, and the transitional column density can be seen as a unique and stable star formation threshold specific to each molecular cloud. These results not only clarify the physical state of Cygnus-X but also emphasize the utility of the N-PDF as a statistical diagnostic tool, as it is an accessible indicator of evolutionary stages and star formation thresholds in molecular clouds.

Cited by 0Open access

The Column Density Probability Density Function of Cygnus-X

Yuchen Xing, Keping Qiu · The Astronomical Journal · 2026

Abstract The density distribution within molecular clouds offers critical insights into their underlying physical processes, which are essential for understanding star formation. As a statistical measure of column density on the cloud scale, the shape and evolution of the column density probability density function (N-PDF) serve as important tools for understanding the dynamics between turbulence and gravity. Here, we investigate the N-PDFs of Cygnus-X using the column density map obtained from Herschel, supplemented by H I and young stellar objects data. We find that the N-PDFs of Cygnus-X and four subregions display log-normal + power-law shapes, indicating the combined effects of turbulence and gravity in sculpting the density structure. We find evidence that the power-law segment of the N-PDFs flattens over time, and the transitional column density can be seen as a unique and stable star formation threshold specific to each molecular cloud. These results not only clarify the physical state of Cygnus-X but also emphasize the utility of the N-PDF as a statistical diagnostic tool, as it is an accessible indicator of evolutionary stages and star formation thresholds in molecular clouds.

Cited by 0Open access

The probability density function of spectral correlation function estimates

Miguel Tavares, J.A.B. Gerald, João Goês · EURASIP Journal on Advances in Signal Processing · 2025

Abstract Since published in 1988, the FFT Accumulation Method (FAM) has been used extensively to compute the Spectral Correlation Function (SCF) and the Spectral Coherence Function (SCoF) to obtain or detect cyclic features of cyclostationary signals. When the input is a Gaussian random variable (r.v.), the SCF (or SCoF) estimates are also random variables with some probability density function (pdf). Although the FAM is considered the most computationally efficient method, there has been no in-depth statistical analysis of the algorithm. This paper analyzes the statistics of spectral estimates of the SCF using the FAM algorithm by obtaining the pdf for the points covering the frequency and cycle frequency $$\left(f;\alpha\right)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mfenced> <mml:mi>f</mml:mi> <mml:mo>;</mml:mo> <mml:mi>α</mml:mi> </mml:mfenced> </mml:math> plane, and application examples with simulation results are provided. The method proposed in the paper can be extended to other algorithms, provided they can be given by a quadratic form.

Cited by 1Open access

New probability density function for biopopulations modelling

Sylvio Péllico Netto, Alexandre Behling · New Zealand journal of forestry science · 2026

Background: Biological populations were studied to understand their ecology and to evaluate the relationships between living beings that comprise them. Mathematical functions used in probabilistic models should present multifunctionality, sensitivity, and flexibility to appropriately describe a natural phenomenon. The objective of this study was to develop a new probabilistic distribution with five parameters to maximize its flexibility and ensure a better goodness of fit when compared to other important distributions, such as Beta, Burr, Silva and Pareto. Methods: New distribution estimators were derived using the mathematical expectation of central and dispersion moments. Estimated values of the parameters were obtained using an optimization process developed by Abel Soares Siqueira, research software engineer at the Netherlands eScience Center in Amsterdam. Data for the application of the developed distribution method were collected at different sites in Brazil, where asymmetry and kurtosis were detected. Results: The Pellico-Behling Probability Distribution (5P) was applied to fit the datasets for Cariniana legalis, Acacia mearnsii, and Eucalyptus saligna. For the average mortality of 124 species, it was used with (4P). The distribution fitted to sampled datasets was compared with the fitted Beta and Burr (4P) distributions, except for Silva’s polynomial distribution that was fitted to the heights of the species Eucalyptus saligna and the Pareto distribution to mortality of 124 tropical species from a fragment of a semideciduous seasonal forest, to evaluate and verify its potential and robustness. Conclusions: The new distribution with five parameters is flexible and produced better goodness of fit than those obtained from the other distributions used for comparative purposes.

Cited by 0Open access