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probability density functions in an asymmetric alluvial sinuous channel

STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT 2025年 1-19页

作者： Gurugubelli, Yatirajulu Timbadiya, P. V. Barman, Bandita Sardar Vallabhbhai Natl Inst Technol Dept Civil Engn Surat 395007 Gujarat India Indian Inst Technol Indian Sch Mines Dept Civil Engn Dhanbad 826004 Jharkhand India

An experimental study examined the probability density functions (PDFs) of flow turbulence in an asymmetric alluvial sinuous channel. Three-dimensional instantaneous velocity measurements were obtained using an acoustic doppler vectrino profiler (ADVP). Results showed higher streamwise velocity near the inner bend due to topographic steering. The streamwise-vertical and streamwise-lateral Reynolds shear stress (RSS) revealed the presence of secondary flow within the bend. Turbulence intensity found to be significant in the streamwise direction than in the vertical direction. The contours of vorticity and lateral velocity vector highlighted the development of helical flow in the bend. The secondary flow drives sediment transport from the outer to the inner bank. A clockwise vorticity core developed in the near-bed region, while counter-clockwise vorticity appeared in the main flow region. The positive vorticity magnitude increased at the bend apex and its upstream but decreased in its downstream. Circulation strength is found to be increased at the upstream of the apex, diminished at the apex, and then again increased in the downstream of the apex. PDFs for flow turbulence parameters, including RSS in the streamwise-vertical and streamwise-lateral directions and turbulence intensity, are compared to theoretical models based on the Gram-Charlier (GC) exponential distribution. Experimental results across all locations showed a strong agreement with the computed PDF distributions.

关键词： Asymmetric sinuous channel Helical flow Vorticity Circulation probability density functions

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probability density functions with Correlations of Experimental and Evaluated ²³⁵U(nth,f) Fission Yields and Their Impacts on Reactivity Loss with Burnup

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NUCLEAR SCIENCE AND ENGINEERING 2025年第sup1期199卷 S507-S520页

作者： Cheikh, S. M. Kessedjian, G. Bernard, D. Serot, O. Chebboubi, A. CEA Cadarache Ctr DES IRESNEDERSPRCLEph F-13108 St Paul Les Durance France

The study of fission yields has a major impact on the characterization and understanding of the fission process and its applications. For the latter, it is crucial to provide fission yields with their associated correlation matrix in order to estimate precisely the uncertainties of crucial quantities, such as the reactivity loss. In the last decade, different works have been proposed to estimate the correlations of the independent fission yields satisfying the consistency of the cumulative yield evaluations. In these previous works, only model parameters and conservation laws have driven the correlations. The novelty of the present work consists of new complete and consistent evaluations of U-235(n(th),f) independent and cumulative yields and their correlation matrices, starting from experimental data. The characterization of the probability density functions of fission yields validates the multivariate Gaussian assumption and constitutes a major issue in the validation of the uncertainty propagation tools of the applications. In addition, the new U-235(n(th),f) fission yield covariance data have resulted in a decrease in nuclear data related to uncertainty in associated burnup calculations.

关键词： Fission yields probability density functions PDF evaluation reactivity losses

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probability density functions of Velocity Increments in the Atmospheric Boundary Layer

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BOUNDARY-LAYER METEOROLOGY 2010年第2期134卷 243-255页

作者： Liu, Lei Hu, Fei Cheng, Xue-Ling Song, Li-Li Chinese Acad Sci Inst Atmospher Phys LAPC Beijing 100029 Peoples R China China Meteorol Adm Inst Trop & Marine Meteorol Guangzhou 510080 Guangdong Peoples R China

The probability density functions (pdf's) of the wind increments are measured under different weather conditions in the atmospheric boundary layer, including the extreme weather of a typhoon and sand storm. It is found that in each case the measured pdf's with respect to different time lags coincide by suitable scaling transformation. This property is similar to that of the stable distributions. However, fitting results show that the tails of the stable distributions are generally heavier than that of the measured ones. Beside, the stable distributions (except for the Gaussian distribution) have infinite variance, which implies infinite average kinetic energy. In fact, it can be proved that if the tails of the pdf's are heavy enough, the variance will be infinite. Therefore, the tail-truncated stable distributions with finite variances are introduced to fit the data and the fitting results are excellent.

关键词： Atmospheric turbulence probability density functions Stable distribution Truncated stable distribution Velocity increments

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probability density functions of amplitude-modulated random signals

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ELECTRONICS LETTERS 1998年第16期34卷 1560-1561页

作者： Cain, GD Lever, KV Yardim, A Univ Westminster Dept Elect Syst London W1M 8JS England Univ S Australia Inst Telecommun Res Adelaide SA 5001 Australia

The probability density function arising from multiplication of two independent random variables has been extensively treated by statisticians, yet some common signal processing product situations have not been analysed. An important example of this omission is the amplitude modulation of a Gaussian process. Here, a little-known Hankel transform-based procedure provides a ready solution for this problem and many other types of random modulation signals. Several new modulation results are tabulated in graphical form and it is also shown that half-amplitude sinusoidal processes added yield the same distribution as their (unit-amplitude) product.

关键词： Integral transforms amplitude modulation Hankel transforms independent random variables Gaussian process probability density functions amplitude-modulated random signals Hankel transform-based procedure Signal processing and detection Information theory half-amplitude sinusoidal processes signal processing Modulation and coding methods probability Other topics in statistics Gaussian processes

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probability density functions describing 24-hour inhalation rates for use in human health risk assessments: An update and comparison

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HUMAN AND ECOLOGICAL RISK ASSESSMENT 2008年第2期14卷 372-391页

作者： Allan, Margaret Richardson, G. Mark Jones-Otazo, Heather Matrix Sollut Inc Calgary AB T2P 0C5 Canada Hlth Canada Ottawa ON K1A 0L2 Canada Hlth Canada Toronto ON Canada

Inhalation rates are used for quantifying inhalation health risks. The time-activity-ventilation (TAV) approach has had longstanding acceptance for estimating inhalation rate (IR) as a time-weighted average across a number of activity levels comprising a typical day. probability density functions (PDFs) describing 24-hour inhalation rates were updated in this study by incorporating supplemental minute volume (Vi) and time-activity (ti) data published since the time of the previous study and by correlating Vi with metabolic equivalents (METs) for the physical activities at the time of measurement. The metabolic correlations are an improvement over the previous study because they enable interpolation to fill data gaps where Vi data are sparse or absent for certain age groups at specific levels of physical activity. The updated PDFs were developed using Monte Carlo simulation and can be described with log normal distributions. The updated PDFs were compared with IR distributions developed through two other approaches: the metabolic energy conversion (MEC) approach;and the doubly labeled water (DLW) approach. Compared to the previous TAV estimates, this study's PDFs suggest lower IR for toddlers and teenagers, higher IR for adults and seniors, and similar IR for infants and children.

关键词： daily inhalation rates time-activity-ventilation human exposure factors probability density functions Monte Carlo simulation metabolic equivalents

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probability density functions as botanical-climatological transfer functions for climate reconstruction

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QUATERNARY RESEARCH 2002年第3期58卷 381-392页

作者： Kühl, N Gebhardt, C Litt, T Hense, A Univ Bonn Inst Paleontol D-53115 Bonn Germany Univ Bonn Inst Meteorol D-53121 Bonn Germany

We present a new procedure, the pdf method (pdf = probability density function), for reconstructing Quaternary climate utilizing botanical data. The procedure includes the advantages of the indicator species method by considering the fossil and modern presence and absence of taxa rather than their frequencies, thus avoiding the need for modern analog plant communities. Overcoming the problematic use of absolute limits to describe climate response ranges is the main progress of the pdf method in comparison to the indicator species method. This advantage results from estimating probability density functions (pdfs) for monthly mean January and July temperature conditional on the present day occurrence of single taxa. Gaussian distributions sufficiently approximate pdfs of many, although not all, studied taxa. On the assumption of statistical independence, the procedure calculates a joint pdf as the product of the pdfs of the individual taxa. This algorithm weights each taxon according to the extent of its climate response range expressed by its covariance structure. We interpret the maximum of the resulting pdf as the most likely climate and its confidence interval as the uncertainty range. To avoid an artificial reduction of uncertainty arising from the use of numerous similar pdfs, a preselection method is proposed based on the Mahalanobis distance between pdfs. The pdf method was applied to the Carpinus phase of a profile from Grobern, Germany, that spans the last interglaciation (Eemian). The reconstructed most probable January and July temperatures of about 0.0degreesC and 18.4degreesC barely differ from the modern values of -0.5degreesC and 18.3degreesC. (C) 2002 University of Washington.

关键词： climate reconstruction Eemian macro remains pollen probability density functions proxy data transfer functions

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probability density functions for Power Output of Wind Electric Conversion Systems

Probability Density Functions for Power Output of Wind Elect...

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IEEE-Power-and-Energy-Society General Meeting

作者： Mohanpurkar, Manish Ramakumar, R. G. Oklahoma State Univ Stillwater OK 74078 USA

ISBN: (纸本)9781424483570

Probabilistic models for the power output of Wind Electric Conversion Systems (WECS) are considered. Wind speeds are modeled using Weibull distribution and probability density function for the power output of WECS is derived using the transformation theorem. Variable portion of the power output characteristic is modeled using different functions and the results are compared. probability density functions for the combined power output of two, four and eight systems are presented and discussed.

关键词： Wind Electric Conversion Weibull distribution Scale parameter Shape parameter probability density functions

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probability density functions of the average and difference intensities of Friedel opposites

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Acta Crystallographica Section A: Foundations of Crystallography 2010年第6期66卷 669-675页

作者： Shmueli, U. Flack, H.D. School of Chemistry Tel Aviv University 69978 Tel Aviv Israel Département de Chimie Minérale Analytique et Appliquée Faculté des Sciences Université de Genve Switzerland

Trigonometric series for the average (A) and difference (D) intensities of Friedel opposites were carefully rederived and were normalized to minimize their dependence on sinν/λ. probability density functions (hereafter p.d.f.s) of these series were then derived by the Fourier method [Shmueli, Weiss, Kiefer & Wilson (1984). Acta Cryst. A40, 651-660] and their expressions, which admit any chemical composition of the unit-cell contents, were obtained for the space group P1. Histograms of A and D were then calculated for an assumed random-structure model and for 3135 Friedel pairs of a published solved crystal structure, and were compared with the p.d.f.s after the latter were scaled up to the histograms. Good agreement was obtained for the random-structure model and a qualitative one for the published solved structure. The results indicate that the residual discrepancy is mainly due to the presumed statistical independence of the p.d.f.s characteristic function on the contributions of the interatomic vectors. © 2010 International Union of Crystallography Printed in Singapore - all rights reserved.

关键词： Friedel opposites interatomic vectors probability density functions trigonometric series

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probability density functions of Logarithmic Likelihood Ratios in Phase Shift Keying BICM

Probability Density Functions of Logarithmic Likelihood Rati...

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IEEE Global Telecommunications Conference (GLOBECOM 06)

作者： Szczecinski, Leszek Benjillali, Mustapha INRS EMT Montreal PQ Canada

ISBN: (纸本)9781424403561

Bit-interleaved coded modulation (BICM) is a coded-modulation scheme where the output of the channel encoder and the input of the modulator are separated by a bit-level interleaver. From the decoder's point of view, the modulator, the transmission channel, and the demodulator (calculating bits' reliability metrics) become a memoryless BICM channel with binary inputs and real outputs. The BICM channel's outputs (reliability metrics) are known to be Gaussian for binary-or quaternary phase shift keying but no expression for their probability density function (PDF) is known for higher-order modulation. We fill this gap presenting closed-form expressions for PDF of reliability metrics in BICM based on M-PSK with Gray mapping. Such probabilistic description of BICM channel is necessary to calculate the channel's information-theoretic parameters such as capacity, or cut-off rate but it is also a tool required to analyze the performance of coded transmission.

关键词： Logarithmic Likelihood Ratios probability density functions Bit-Interleaved Coded Modulation Phase-Shift Keying LLR PDF BICM PSK

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An approximation of small-time probability density functions in a general jump diffusion model

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APPLIED MATHEMATICS AND COMPUTATION 2016年 273卷 741-758页

作者： Zhang, Le Schmidt, Wolfgang M. Frankfurt Sch Finance & Management D-06031 Frankfurt Germany

We propose a method for approximating probability density functions related to multidimensional jump diffusion processes. For small-time horizons, a closed-form approximation of the characteristic function is derived based on the Ito-Taylor expansion. The probability density function is then approximated numerically by inverting the characteristic function using fast Fourier transform. As application we consider a general stochastic volatility model, which involves time-/state-dependent drift and diffusion functions as well as jump components. We test our approach under the Heston model and the Bates model and show that our method provides accurate approximations. (C) 2015 Elsevier Inc. All rights reserved.

关键词： Jump diffusion process Ito-Taylor expansions Stochastic volatility models Characteristic functions probability density functions

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