Is it Possible to Replace the Probability Distribution Function Describing a Random Process by the Prony’s Spectrum? (I)

2012 ◽  
Vol 1 (2) ◽  
pp. 173-194 ◽  
Author(s):  
Raoul R. Nigmatullin
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Random Process ◽  
Probability Distribution Function

Extreme Values of Waves and Ship Responses Subject to the Markov Chain Condition

1979 ◽  
Vol 23 (03) ◽  
pp. 188-197
Author(s):  
Michel K. Ochi
Keyword(s):  
Distribution Function ◽  
Markov Chain ◽  
Probability Distribution ◽  
Random Process ◽  
Probability Distribution Function ◽  
Extreme Values ◽  
Random Processes ◽  
Chain Condition ◽  
Extreme Value ◽  
Spectral Bandwidth

This paper discusses the effect of statistical dependence of the maxima (peak values) of a stationary random process on the magnitude of the extreme values. A theoretical analysis of the extreme values of a stationary normal random process is made, assuming the maxima are subject to the Markov chain condition. For this, the probability distribution function of maxima as well as the joint probability distribution function of two successive maxima of a normal process having an arbitrary spectral bandwidth are applied to Epstein's theorem for evaluating the extreme values in a given sample under the Markov chain condition. A numerical evaluation of the extreme values is then carried out for a total of 14 random processes, including nine ocean wave records, with various spectral bandwidth parameters ranging from 0.11 to 0.78. From the results of the computations, it is concluded that the Markov concept is applicable to the maxima of random processes whose spectral bandwidth parameter, ɛ, is less than 0.5, and that the extreme values with and without the Markov concept are constant irrespective of the e-value, and the former is approximately 10 percent greater than the latter. It is also found that the sample size for which the extreme value reaches a certain level with the Markov concept is much less than that without the Markov concept. For example, the extreme value will reach a level of 4.0 (nondimensional value) in 1100 observations of the maxima with the Markov concept, while the extreme value will reach the same level in 3200 observations of the maxima without the Markov concept.

scholarly journals An Online Application for ΔR Calculation

Radiocarbon ◽  
2016 ◽  
Vol 59 (5) ◽  
pp. 1623-1627 ◽  
Author(s):  
Ron W Reimer ◽  
Paula J Reimer
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Calibration Curve ◽  
Probability Distribution Function ◽  
Museum Collections ◽  
Online Program ◽  
Online Application ◽  
Radiocarbon Calibration

AbstractA regional offset (ΔR) from the marine radiocarbon calibration curve is widely used in calibration software (e.g. CALIB, OxCal) but often is not calculated correctly. While relatively straightforward for known-age samples, such as mollusks from museum collections or annually banded corals, it is more difficult to calculate ΔR and the uncertainty in ΔR for 14C dates on paired marine and terrestrial samples. Previous researchers have often utilized classical intercept methods that do not account for the full calibrated probability distribution function (pdf). Recently, Soulet (2015) provided R code for calculating reservoir ages using the pdfs, but did not address ΔR and the uncertainty in ΔR. We have developed an online application for performing these calculations for known-age, paired marine and terrestrial 14C dates and U-Th dated corals. This article briefly discusses methods that have been used for calculating ΔR and the uncertainty and describes the online program deltar, which is available free of charge.

scholarly journals Optimal Taylor–Couette turbulence

2012 ◽  
Vol 706 ◽  
pp. 118-149 ◽  
Author(s):  
Dennis P. M. van Gils ◽  
Sander G. Huisman ◽  
Siegfried Grossmann ◽  
Chao Sun ◽  
Detlef Lohse
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Angular Velocity ◽  
Probability Distribution Function ◽  
Neutral Line ◽  
Velocity Ratio ◽  
Outer Cylinder ◽  
Taylor Number ◽  
Counter Rotation ◽  
Taylor Couette

AbstractStrongly turbulent Taylor–Couette flow with independently rotating inner and outer cylinders with a radius ratio of $\eta = 0. 716$ is experimentally studied. From global torque measurements, we analyse the dimensionless angular velocity flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)$ as a function of the Taylor number $\mathit{Ta}$ and the angular velocity ratio $a= \ensuremath{-} {\omega }_{o} / {\omega }_{i} $ in the large-Taylor-number regime $1{0}^{11} \lesssim \mathit{Ta}\lesssim 1{0}^{13} $ and well off the inviscid stability borders (Rayleigh lines) $a= \ensuremath{-} {\eta }^{2} $ for co-rotation and $a= \infty $ for counter-rotation. We analyse the data with the common power-law ansatz for the dimensionless angular velocity transport flux ${\mathit{Nu}}_{\omega } (\mathit{Ta}, a)= f(a)\hspace{0.167em} {\mathit{Ta}}^{\gamma } $, with an amplitude $f(a)$ and an exponent $\gamma $. The data are consistent with one effective exponent $\gamma = 0. 39\pm 0. 03$ for all $a$, but we discuss a possible $a$ dependence in the co- and weakly counter-rotating regimes. The amplitude of the angular velocity flux $f(a)\equiv {\mathit{Nu}}_{\omega } (\mathit{Ta}, a)/ {\mathit{Ta}}^{0. 39} $ is measured to be maximal at slight counter-rotation, namely at an angular velocity ratio of ${a}_{\mathit{opt}} = 0. 33\pm 0. 04$, i.e. along the line ${\omega }_{o} = \ensuremath{-} 0. 33{\omega }_{i} $. This value is theoretically interpreted as the result of a competition between the destabilizing inner cylinder rotation and the stabilizing but shear-enhancing outer cylinder counter-rotation. With the help of laser Doppler anemometry, we provide angular velocity profiles and in particular identify the radial position ${r}_{n} $ of the neutral line, defined by $ \mathop{ \langle \omega ({r}_{n} )\rangle } \nolimits _{t} = 0$ for fixed height $z$. For these large $\mathit{Ta}$ values, the ratio $a\approx 0. 40$, which is close to ${a}_{\mathit{opt}} = 0. 33$, is distinguished by a zero angular velocity gradient $\partial \omega / \partial r= 0$ in the bulk. While for moderate counter-rotation $\ensuremath{-} 0. 40{\omega }_{i} \lesssim {\omega }_{o} \lt 0$, the neutral line still remains close to the outer cylinder and the probability distribution function of the bulk angular velocity is observed to be monomodal. For stronger counter-rotation the neutral line is pushed inwards towards the inner cylinder; in this regime the probability distribution function of the bulk angular velocity becomes bimodal, reflecting intermittent bursts of turbulent structures beyond the neutral line into the outer flow domain, which otherwise is stabilized by the counter-rotating outer cylinder. Finally, a hypothesis is offered allowing a unifying view and consistent interpretation for all these various results.

Audio feature extraction using probability distribution function

2015 ◽  
Author(s):  
Suhaib A. ◽  
Khairunizam Wan ◽  
Azri A. Aziz ◽  
D. Hazry ◽  
Zuradzman M. Razlan ◽  
...  
Keyword(s):  
Feature Extraction ◽  
Distribution Function ◽  
Probability Distribution ◽  
Probability Distribution Function ◽  
Audio Feature ◽  
Audio Feature Extraction
Sign in / Sign up

Export Citation Format

Share Document