A Simple Approximation for the Bivariate Normal Integral

1995 ◽  
Vol 9 (2) ◽  
pp. 317-321 ◽  
Author(s):  
Jinn-Tyan Lin
Keyword(s):  
Simple Approximation ◽  
Elementary Functions ◽  
Bivariate Normal

Approximations for the univariate normal integral are employed to develop a simple approximation in terms of elementary functions for the bivariate normal integral. The accuracy of the approximation is quite sufficient for many practical cases.

Simple approximation of sample size for the bivariate normal

1989 ◽  
Vol 8 (2) ◽  
pp. 201-207 ◽  
Author(s):  
Neil C. Schwertman ◽  
Margaret A. Owens
Keyword(s):  
Sample Size ◽  
Simple Approximation ◽  
Bivariate Normal

A note on the generalization of bivariate normal quadrant probabilities to bivariate elliptical distributions

2018 ◽  
Author(s):  
Oscar Lorenzo Olvera Astivia
Keyword(s):  
Normal Distribution ◽  
Bivariate Normal Distribution ◽  
Elliptical Distributions ◽  
Bivariate Normal ◽  
Geometric Argument

I present a geometric argument to show that the quadrant probability for the bivariate normal distribution can be generalized to the case of all elliptical distributions.

Simple Approximation to Diffraction-Limited MTF

1971 ◽  
Vol 10 (11) ◽  
pp. 2547_1
Author(s):  
R. E. Hufnagel
Keyword(s):  
Simple Approximation

M-groupoid as a tool for investigating mathematical models of computers

1977 ◽  
Vol 1 (1) ◽  
pp. 71-91
Author(s):  
Jerzy Tiuryn
Keyword(s):  
Mathematical Models ◽  
Simple Approximation ◽  
Simplified Model ◽  
Suitable Choice ◽  
Iterative Systems

An M-groupoid is a simplified model of computer. The classes of M-groupoids, address machines, stored program computers and iterative systems are presented as categories – by a suitable choice of homomorphisms. It is shown that the first three categories are equivalent, whereas the fourth is weaker (it is not equivalent to the previous ones and it can easily be embedded in the category of M-groupoids). This fact proves that M-groupoids form an essentially better and reasonably simple approximation of more complicated models of computers than iterative systems.

scholarly journals Second-order integrable Lagrangians and WDVV equations

2021 ◽  
Vol 111 (2) ◽  
Author(s):  
E. V. Ferapontov ◽  
M. V. Pavlov ◽  
Lingling Xue
Keyword(s):  
Lagrangian Density ◽  
Theta Functions ◽  
Second Order ◽  
Elementary Functions ◽  
Lagrange Equations ◽  
Wdvv Equations ◽  
Integrability Conditions ◽  
Jacobi Theta Functions

AbstractWe investigate the integrability of Euler–Lagrange equations associated with 2D second-order Lagrangians of the form $$\begin{aligned} \int f(u_{xx},u_{xy},u_{yy})\ \mathrm{d}x\mathrm{d}y. \end{aligned}$$ ∫ f ( u xx , u xy , u yy ) d x d y . By deriving integrability conditions for the Lagrangian density f, examples of integrable Lagrangians expressible via elementary functions, Jacobi theta functions and dilogarithms are constructed. A link of second-order integrable Lagrangians to WDVV equations is established. Generalisations to 3D second-order integrable Lagrangians are also discussed.

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