Bivariate Normal Distribution

2011 ◽  
Keyword(s):  
Normal Distribution ◽  
Bivariate Normal Distribution ◽  
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.

scholarly journals PSIII-5 Comparison of Bivariate Machine Learning and Linear Model for Genomic Prediction with Different Heritability, QTL and SNP Panel Scenarios

2020 ◽  
Vol 98 (Supplement_4) ◽  
pp. 230-231
Author(s):  
Sunday O Peters ◽  
Mahmut Sinecan ◽  
Kadir Kizilkaya ◽  
Milt Thomas
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
Normal Distribution ◽  
Genomic Prediction ◽  
Network Models ◽  
Bivariate Normal Distribution ◽  
Snp Markers ◽  
Neural Network Models ◽  
Bivariate Normal ◽  
Artificial Neural

Abstract This simulation study used actual SNP genotypes on the first chromosome of Brangus beef cattle to simulate 0.50 genetically correlated two traits with heritabilities of 0.25 and 0.50 determined either by 50, 100, 250 or 500 QTL and then aimed to compare the accuracies of genomic prediction from bivariate linear and artificial neural network with 1 to 10 neurons models based on G genomic relationship matrix. QTL effects of 50, 100, 250 and 500 SNPs from the 3361 SNPs of 719 animals were sampled from a bivariate normal distribution. In each QTL scenario, the breeding values (Σgijβj) of animal i for two traits were generated by using genotype (gij) of animal i at QTL j and the effects (βj) of QTL j from a bivariate normal distribution. Phenotypic values of animal i for traits were generated by adding residuals from a bivariate normal distribution to the breeding values of animal i. Genomic predictions for traits were carried out by bivariate Feed Forward MultiLayer Perceptron ANN-1–10 neurons and linear (GBLUP) models. Three sets of SNP panels were used for genomic prediction: only QTL genotypes (Panel1), all SNP markers, including the QTL (Panel2), and all SNP markers, excluding the QTL (Panel3). Correlations from 10-fold cross validation for traits were used to assess predictive ability of bivariate linear (GBLUP) and artificial neural network models based on 4 QTL scenarios with 3 Panels of SNP panels. Table 1 shows that the trait with high heritability (0.50) resulted in higher correlation than the trait with low heritability (0.25) in bivariate linear (GBLUP) and artificial neural network models. However, bivariate linear (GBLUP) model produced higher correlation than bivariate neural network. Panel1 performed the best correlations for all QTL scenarios, then Panel2 including QTL and SNP markers resulted in better prediction than Panel3.

Tables of the Integral of the Elliptical Bivariate Normal Distribution over Offset Circles.

1962 ◽  
Vol 16 (77) ◽  
pp. 116
Author(s):  
Author's Summary ◽  
G. W. Rosenthal ◽  
J. J. Rodden
Keyword(s):  
Normal Distribution ◽  
Bivariate Normal Distribution ◽  
Bivariate Normal

Computation of the Integral of the Bivariate Normal Distribution Over Convex Polygons

1980 ◽  
Vol 1 (2) ◽  
pp. 179-186 ◽  
Author(s):  
A. R. Didonato ◽  
M. P. Jarnagin, Jr. ◽  
R. K. Hageman
Keyword(s):  
Normal Distribution ◽  
Bivariate Normal Distribution ◽  
Convex Polygons ◽  
Bivariate Normal

Dual-Issue Final-Offer Arbitration: Invariance of Pure Optimal Strategies Under Lp Metrics

2019 ◽  
Vol 21 (04) ◽  
pp. 1950011
Author(s):  
Brian R. Powers
Keyword(s):  
Normal Distribution ◽  
Optimal Strategies ◽  
Bivariate Normal Distribution ◽  
Bivariate Normal ◽  
Final Offer ◽  
Pure Strategies ◽  
Zero Sum

We consider a final-offer arbitration problem between two players with two quantitative issues in dispute. We model the problem as a zero-sum game where the arbiter’s opinion is drawn from a bivariate normal distribution and derive the only possible pure strategies regardless of the choice of [Formula: see text] metric used by the arbiter.

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