Digital simulation of two-dimensional random fields with arbitrary power spectra and non-Gaussian probability distribution functions

Mathematics and computer science are interested in methods of 2D curve interpolation and extrapolation using the set of key points (knots or nodes). Proposed method, called by author Probabilistic Nodes Combination (PNC), is such a method. This novel PNC method is introduced in the case of Hurwitz- Radon Matrices (MHR). MHR method is based on the family of Hurwitz-Radon (HR) matrices which possess columns composed of orthogonal vectors. Two-dimensional curve is modeled and interpolated via different functions as probability distribution functions: polynomial, sinus, cosine, tangent, cotangent, logarithm, exponent, arcsin, arccos, arctan, arcctg or power function, also inverse functions. It is shown how to build the orthogonal matrix operator and how to use it in a process of curve reconstruction.

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Probability Distribution of the Eigenvalues of the Random String Equation

Journal of Applied Mechanics ◽

10.1115/1.3176047 ◽

1989 ◽

Vol 56 (1) ◽

pp. 202-207 ◽

Cited By ~ 10

Author(s):

R. N. Iyengar ◽

C. S. Manohar

Keyword(s):

Probability Distribution ◽

Digital Simulation ◽

Distribution Functions ◽

Random String ◽

Initial Value ◽

Numerical Work ◽

First Order ◽

Probability Distribution Functions ◽

Nonlinear Stochastic Differential Equation ◽

Stochastic Boundary

The probability distribution of the eigenvalues of a second-order stochastic boundary value problem is considered. The solution is characterized in terms of the zeros of an associated initial value problem. It is further shown that the probability distribution is related to the solution of a first-order nonlinear stochastic differential equation. Solutions of this equation based on the theory of Markov processes and also on the closure approximation are presented. A string with stochastic mass distribution is considered as an example for numerical work. The theoretical probability distribution functions are compared with digital simulation results. The comparison is found to be reasonably good.

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Extended two-dimensional belief function based on divergence measurement

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-201727 ◽

2020 ◽

pp. 1-8

Author(s):

Jianping Fan ◽

Jing Wang ◽

Meiqin Wu

Keyword(s):

Belief Function ◽

Distribution Functions ◽

Divergence Measure ◽

Uncertain Information ◽

Belief Functions ◽

Two Dimensional ◽

Probability Distribution Functions ◽

Basic Probability ◽

The Difference ◽

Supporting Degree

The two-dimensional belief function (TDBF = (mA, mB)) uses a pair of ordered basic probability distribution functions to describe and process uncertain information. Among them, mB includes support degree, non-support degree and reliability unmeasured degree of mA. So it is more abundant and reasonable than the traditional discount coefficient and expresses the evaluation value of experts. However, only considering that the expert’s assessment is single and one-sided, we also need to consider the influence between the belief function itself. The difference in belief function can measure the difference between two belief functions, based on which the supporting degree, non-supporting degree and unmeasured degree of reliability of the evidence are calculated. Based on the divergence measure of belief function, this paper proposes an extended two-dimensional belief function, which can solve some evidence conflict problems and is more objective and better solve a class of problems that TDBF cannot handle. Finally, numerical examples illustrate its effectiveness and rationality.

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