The probability contours and a goodness-of-fit test for the singly truncated bivariate normal distribution

1978 ◽  
Vol 7 (6) ◽  
pp. 557-572 ◽  
Author(s):  
Marshall N. Brunden
Keyword(s):  
Normal Distribution ◽  
Goodness Of Fit ◽  
Bivariate Normal Distribution ◽  
Goodness Of Fit Test ◽  
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

scholarly journals PEMILIHAN DISTRIBUSI PROBABILITAS PADA ANALISA HUJAN DENGAN METODE GOODNESS OF FIT TEST

2016 ◽  
Vol 18 (2) ◽  
pp. 139-148
Author(s):  
Togani Cahyadi Upomo ◽  
Rini Kusumawardani
Keyword(s):  
Normal Distribution ◽  
Goodness Of Fit ◽  
Gumbel Distribution ◽  
Rainfall Event ◽  
Goodness Of Fit Test ◽  
Chi Square ◽  
Chi Square Test ◽  
Log Normal ◽  
Log Normal Distribution ◽  
Pearson Iii Distribution

Rainfall event is a stochastic process, so to explain and analyze this processes the probability theory and frequency analysisare used. There are four types of probability distributions.They are normal, log normal, log Pearson III and Gumbel. To find the best probabilities distribution, it will used goodness of fit test. The tests consist of chi-square and smirnov-kolmogorov. Results of the chi-square test for normal distribution, log normal and log Pearson III was 0.200, while for the Gumbel distribution was 2.333. Results of Smirnov Kolmogorov test for normal distribution D = 0.1554, log-normal distribution D = 0.1103, log Pearson III distribution D = 0.1177 and Gumbel distribution D = 0.095. All of the distribution can be accepted with a confidence level of 95%, but the best distribution is log normal distribution.Kejadian hujan merupakan proses stokastik, sehingga untuk keperluan analisa dan menjelaskan proses stokastik tersebut digunakan teori probabilitas dan analisa frekuensi. Terdapat empat jenis distribusi probabilitas yaitu distribusi normal, log normal, log pearson III dan gumbel. Untuk mencari distribusi probabilitas terbaik maka akan digunakan pengujian metode goodness of fit test. Pengujian tersebut meliputi uji chi-kuadrat dan uji smirnov kolmogorov. Hasil pengujian chi kuadrat untuk distribusi normal, log normal dan log pearson III adalah 0.200, sedangkan untuk distribusi gumbel 2.333. Hasil pengujian smirnov kolmogorov untuk distribusi normal dengan nilai D = 0.1554, distribusi log normal dengan nilai D = 0.1103, distribusi log pearson III dengan nilai D = 0.1177 dan distribusi gumbel dengan nilai D = 0.095. Seluruh distribusi dapat diterima dengan tingkat kepercayaan 95%, tetapi distribusi terbaik adalah distribusi log normal.

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