The Closed-Form Steady-State Probability Density Function of van der Pol Oscillator under Random Excitations

2016 ◽  
Vol 5 (4) ◽  
pp. 495-502
Author(s):  
Lincong Chen ◽  
Jian-Qiao Sun
Keyword(s):  
Steady State ◽  
Probability Density Function ◽  
Closed Form ◽  
Probability Density ◽  
Density Function ◽  
Van Der Pol Oscillator ◽  
State Probability ◽  
Van Der Pol ◽  
Steady State Probability

scholarly journals On the Density and Moments of the Time of Ruin with Exponential Claims

2003 ◽  
Vol 33 (1) ◽  
pp. 11-21 ◽  
Author(s):  
Steve Drekic ◽  
Gordon E. Willmot
Keyword(s):  
Probability Density Function ◽  
Laplace Transform ◽  
Closed Form ◽  
Probability Density ◽  
Density Function ◽  
Classical Model ◽  
Time Of Ruin ◽  
The Time Of Ruin

The probability density function of the time of ruin in the classical model with exponential claim sizes is obtained directly by inversion of the associated Laplace transform. This result is then used to obtain explicit closed-form expressions for the moments. The form of the density is examined for various parameter choices.

A CLOSED FORM FOR THE DENSITY FUNCTIONS OF RANDOM WALKS IN ODD DIMENSIONS

2015 ◽  
Vol 93 (2) ◽  
pp. 330-339 ◽  
Author(s):  
JONATHAN M. BORWEIN ◽  
CORWIN W. SINNAMON
Keyword(s):  
Random Walk ◽  
Probability Density Function ◽  
Random Walks ◽  
Closed Form ◽  
Probability Density ◽  
Density Function ◽  
Dimensional Space ◽  
Density Functions ◽  
Piecewise Polynomial ◽  
Odd Dimensions

We derive an explicit piecewise-polynomial closed form for the probability density function of the distance travelled by a uniform random walk in an odd-dimensional space.

scholarly journals On the Density and Moments of the Time of Ruin with Exponential Claims

2003 ◽  
Vol 33 (01) ◽  
pp. 11-21 ◽  
Author(s):  
Steve Drekic ◽  
Gordon E. Willmot
Keyword(s):  
Probability Density Function ◽  
Laplace Transform ◽  
Closed Form ◽  
Probability Density ◽  
Density Function ◽  
Classical Model ◽  
Time Of Ruin ◽  
The Time Of Ruin

The probability density function of the time of ruin in the classical model with exponential claim sizes is obtained directly by inversion of the associated Laplace transform. This result is then used to obtain explicit closed-form expressions for the moments. The form of the density is examined for various parameter choices.

scholarly journals A Novel Limit Distribution for the Analysis of Randomly Mistuned Bladed Disks

1996 ◽  
Author(s):  
Marc P. Mignolet ◽  
Chung-Chih Lin
Keyword(s):  
Steady State ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Perturbation Technique ◽  
Practical Case ◽  
Numerical Examples ◽  
Critical Effect ◽  
Form Model ◽  
Steady State Amplitude

A recently introduced perturbation technique is employed to derive a novel closed form model for the probability density function of the resonant and near-resonant, steady state amplitude of blade response in randomly mistuned disks. In its most general form, this model is shown to involve six parameters but, in the important practical case of a pure stiffness (or frequency) mistuning, only three parameters are usually sufficient to completely specify this distribution. A series of numerical examples are presented that demonstrate the extreme reliability of this three-parameter model in accurately predicting the entire probability density function of the amplitude of response, and in particular the large amplitude tail of this distribution which is the most critical effect of mistuning.

A Novel Limit Distribution for the Analysis of Randomly Mistuned Bladed Disks1

2000 ◽  
Vol 123 (2) ◽  
pp. 388-394 ◽  
Author(s):  
M. P. Mignolet ◽  
C.-C. Lin ◽  
B. H. LaBorde
Keyword(s):  
Steady State ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Perturbation Technique ◽  
Practical Case ◽  
Numerical Examples ◽  
Critical Effect ◽  
Form Model ◽  
Steady State Amplitude

A recently introduced perturbation technique is employed to derive a novel closed form model for the probability density function of the resonant and near-resonant, steady state amplitude of blade response in randomly mistuned disks. In its most general form, this model is shown to involve six parameters but, in the important practical case of a pure stiffness (or frequency) mistuning, only three parameters are usually sufficient to completely specify this distribution. A series of numerical examples are presented that demonstrate the reliability of this three-parameter model in accurately predicting the entire probability density function of the amplitude of response, and in particular the large amplitude tail of this distribution, which is the most critical effect of mistuning.

An approximate technique for determining in closed form the response transition probability density function of diverse nonlinear/hysteretic oscillators

2019 ◽  
Vol 97 (4) ◽  
pp. 2627-2641 ◽  
Author(s):  
Antonios T. Meimaris ◽  
Ioannis A. Kougioumtzoglou ◽  
Athanasios A. Pantelous ◽  
Antonina Pirrotta
Keyword(s):  
Probability Density Function ◽  
Closed Form ◽  
Probability Density ◽  
Density Function ◽  
Transition Probability ◽  
Transition Probability Density

scholarly journals A NOTE CONCERNING THE DISTANCES OF UNIFORMLY DISTRIBUTED POINTS FROM THE CENTRE OF A RECTANGLE

2012 ◽  
Vol 87 (1) ◽  
pp. 115-119 ◽  
Author(s):  
ROBERT STEWART ◽  
HONG ZHANG
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Closed Form ◽  
Probability Density ◽  
Density Function ◽  
Cumulative Distribution Function ◽  
Average Distance ◽  
Cumulative Distribution

AbstractGiven a rectangle containing uniformly distributed random points, how far are the points from the rectangle’s centre? In this paper we provide closed-form expressions for the cumulative distribution function and probability density function that characterise the distance. An expression for the average distance to the centre of the rectangle is also provided.

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