scholarly journals Image Denoising Based on Bivariate Distribution

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1909
Author(s):  
Ping Zhao ◽  
Xingyu Zhao ◽  
Chun Zhao
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Estimation Method ◽  
Cauchy Distribution ◽  
Bivariate Distribution ◽  
Complex Wavelet Transform ◽  
Shrinkage Function ◽  
Special Cases ◽  
Integration Techniques

The literature has shown that the performance of the de-noising algorithm was greatly influenced by the dependencies between wavelet coefficients. In this paper, the bivariate probability density function (PDF) was proposed which was symmetric, and the dependencies between the coefficients were considered. The bivariate Cauchy distribution and the bivariate Student’s distribution are special cases of the proposed bivariate PDF. One of the parameters in the probability density function gave the estimation method, and the other parameter can take any real number greater than 2. The algorithm adopted a maximum a posteriori estimator employing the dual-tree complex wavelet transform (DTCWT). Compared with the existing best results, the method is faster and more efficient than the previous numerical integration techniques. The bivariate shrinkage function of the proposed algorithm can be expressed explicitly. The proposed method is simple to implement.

scholarly journals On The Distribution Of Mixed Sum Of Independent Random Variables One Of Them Associated With Srivastava's Polynomials And H -Function

2014 ◽  
Vol 10 (1) ◽  
pp. 53-62 ◽  
Author(s):  
Jagdev Singh ◽  
Devendra Kumar
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Random Variables ◽  
Probability Density Functions ◽  
Independent Random Variables ◽  
Special Cases ◽  
The Laplace Transform ◽  
Srivastava’S Polynomials ◽  
Infinite Range

Abstract In this paper, we obtain the distribution of mixed sum of two independent random variables with different probability density functions. One with probability density function defined in finite range and the other with probability density function defined in infinite range and associated with product of Srivastava's polynomials and H-function. We use the Laplace transform and its inverse to obtain our main result. The result obtained here is quite general in nature and is capable of yielding a large number of corresponding new and known results merely by specializing the parameters involved therein. To illustrate, some special cases of our main result are also given.

scholarly journals Bivariate Burr Type III Distribution: Estimation and Prediction

2021 ◽  
pp. 16-36
Author(s):  
A. A. M. Mahmoud ◽  
R. M. Refaey ◽  
G. R. AL-Dayian ◽  
A. A. EL-Helbawy
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Real Life ◽  
Bivariate Distribution ◽  
Cumulative Distribution ◽  
Data Set ◽  
Squared Error Loss Function ◽  
Type Iii ◽  
Estimation And Prediction

In this paper, a bivariate Burr Type III distribution is constructed and some of its statistical properties such as bivariate probability density function and its marginal, joint cumulative distribution and its marginal, reliability and hazard rate functions are studied. The joint probability density function and the joint cumulative distribution are given in closed forms. The joint expectation of this distribution is proposed. The maximum likelihood estimation and prediction for a future observation are derived. Also, Bayesian estimation and prediction are considered under squared error loss function. The performance of the proposed bivariate distribution is examined using a simulation study. Finally, a data set is analyzed under the proposed distribution to illustrate its flexibility for real-life application.

scholarly journals A systematic path to non-Markovian dynamics: new response probability density function evolution equations under Gaussian coloured noise excitation

2019 ◽  
Vol 475 (2226) ◽  
pp. 20180837 ◽  
Author(s):  
K. I. Mamis ◽  
G. A. Athanassoulis ◽  
Z. G. Kapelonis
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Evolution Equations ◽  
Stochastic Dynamics ◽  
Time History ◽  
Multidimensional Case ◽  
Coloured Noise ◽  
Special Cases ◽  
Non Locality

Determining evolution equations governing the probability density function (pdf) of non-Markovian responses to random differential equations (RDEs) excited by coloured noise, is an important issue arising in various problems of stochastic dynamics, advanced statistical physics and uncertainty quantification of macroscopic systems. In the present work, such equations are derived for a scalar, nonlinear RDE under additive coloured Gaussian noise excitation, through the stochastic Liouville equation. The latter is an exact, yet non-closed equation, involving averages over the time history of the non-Markovian response. This non-locality is treated by applying an extension of the Novikov–Furutsu theorem and a novel approximation, employing a stochastic Volterra–Taylor functional expansion around instantaneous response moments, leading to efficient, closed, approximate equations for the response pdf. These equations retain a tractable amount of non-locality and nonlinearity, and they are valid in both the transient and long-time regimes for any correlation function of the excitation. Also, they include as special cases various existing relevant models, and generalize Hänggi's ansatz in a rational way. Numerical results for a bistable nonlinear RDE confirm the accuracy and the efficiency of the new equations. Extension to the multidimensional case (systems of RDEs) is feasible, yet laborious.

scholarly journals Construction of Reducible Stochastic Differential Equation Systems for Tree Height–Diameter Connections

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1363 ◽  
Author(s):  
Martynas Narmontas ◽  
Petras Rupšys ◽  
Edmundas Petrauskas
Keyword(s):  
Differential Equation ◽  
Probability Density Function ◽  
Stochastic Differential Equation ◽  
Probability Density ◽  
Density Function ◽  
Tree Height ◽  
Bivariate Distribution ◽  
General Purpose ◽  
Mixed Effect ◽  
Bivariate Probability

This study proposes a general bivariate stochastic differential equation model of population growth which includes random forces governing the dynamics of the bivariate distribution of size variables. The dynamics of the bivariate probability density function of the size variables in a population are described by the mixed-effect parameters Vasicek, Gompertz, Bertalanffy, and the gamma-type bivariate stochastic differential equations (SDEs). The newly derived bivariate probability density function and its marginal univariate, as well as the conditional univariate function, can be applied for the modeling of population attributes such as the mean value, quantiles, and much more. The models presented here are the basis for further developments toward the tree diameter–height and height–diameter relationships for general purpose in forest management. The present study experimentally confirms the effectiveness of using bivariate SDEs to reconstruct diameter–height and height–diameter relationships by using measurements obtained from mountain pine tree (Pinus mugo Turra) species dataset in Lithuania.

Nonlinear Roll Damping With Coupling Effect in Regular Beam-Wave

2021 ◽  
Author(s):  
Peyman Asgari ◽  
Antonio Carlos Fernandes
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Coupling Effect ◽  
Cauchy Distribution ◽  
Roll Damping ◽  
Straight Line ◽  
Roll System ◽  
First Time ◽  
Well Posed

Abstract Despite of numbers of method to estimate and predict the nonlinear roll damping, it is the mode least understood and the most difficult to determine so far. Reviewing the existing methods reveals that the coupling effects of other modes on roll motion are ignored by assuming just one degree of freedom (1DOF) roll in experiments. The new concept of Most Often Instantaneous Rotation Center - MOIRC proposed by Fernandes and Asgari has brough other parameters, which can help us to improve the roll damping analysis by including the coupling (roll-sway) that results in asymmetric roll responses. This paper, by describing experiments, aims to confirm this roll-sway effect on roll damping coefficient by taking a well posed 3DOF, which allows to follow the instantaneous rotation centers - IRCs. The regular beam-waves experiments were conducted for different frequencies and wave amplitudes. A 3DOF (sway, heave and roll) system identification is used to extract roll damping from the model test. It is shown that the locus of the IRCs follows a straight line and it has a statistical behavior whose probability density function of IRCs with a Cauchy probability density function. For the first time this characteristic is provided experimentally, well matching with the analytical Cauchy distribution.

Probability Model of Beijing Residentials’ Fire Load

2011 ◽  
Vol 368-373 ◽  
pp. 993-1002 ◽  
Author(s):  
Yan Chao Liu ◽  
Dong Dong Liu ◽  
Jin Ping Wang ◽  
Wei Hong Chen ◽  
Bin Zhao
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Probability Model ◽  
Estimation Method ◽  
Extreme Value Distribution ◽  
Likelihood Estimation ◽  
Generalized Extreme Value Distribution ◽  
Fire Load ◽  
Distribution Models

We analyses 418 of fire load data of Beijing residential in city subdivision and suburban district which collected by Beijing University of Civil Engineering and Architecture and Institute of Building Fire Research. Suppose the probability density function of several fire load, using maximum likelihood estimation method to obtain the parameters, and use the K-S test examine the probability density function model, the final selections of Generalized extreme value distribution and Log logistic fit better as a Beijing residential fire load distribution probability distribution models. Finally using these models, according to the JCSS rules, the fire load standard value of Beijing residential is put forward.

Fully Nonparametric Probability Density Function Estimation Based on Empirical Mode Decomposition

2012 ◽  
Vol 460 ◽  
pp. 189-192
Author(s):  
Hong Ying Hu ◽  
Chun Ming Kan
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Density Estimation ◽  
Empirical Mode Decomposition ◽  
Estimation Method ◽  
Function Estimation ◽  
Mode Decomposition ◽  
Non Stationary Signal ◽  
Density Function Estimation

Empirical Mode Decomposition (EMD) is a non-stationary signal processing method developed recently. It has been applied in many engineering fields. EMD has many similarities with wavelet decomposition. But EMD Decomposition has its own characteristics, especially in accurate rend extracting. Therefore the paper firstly proposes an algorithm of extracting slow-varying trend based on EMD. Then, according to wavelet probability density function estimation method, a new density estimation method based on EMD is presented. The simulations of Gaussian single and mixture model density estimation prove the advantages of the approach with easy computation and more accurate result

A points estimation and series approximation method for uncertainty analysis

2009 ◽  
Vol 223 (9) ◽  
pp. 1997-2007 ◽  
Author(s):  
X F Zhang ◽  
Y E Zhao ◽  
Y M Zhang ◽  
X Z Huang ◽  
H Li
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Function Approximation ◽  
Structural Reliability ◽  
Estimation Method ◽  
Point Estimation ◽  
Performance Function ◽  
Density Function Approximation ◽  
Point Estimation Method

The objective of this article is to present an algorithm for moment evaluation and probability density function approximation of performance function for structural reliability analysis. In doing so, a point estimation method for probability moment of performance function is discussed at first. Based on the coherent relationship between the orthogonal polynomial and probability density function, formulas for point estimation are derived. Vector operators are defined to alleviate computational burden for computer programming. Then, by utilizing C-type Gram—Charlier series expansion method, a procedure for probability density function approximation of the performance function is studied. At last, the accuracy of the proposed method is demonstrated using three numerical examples.

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