What Everyone Should Know: About Univariate Normality and Bivariate Normality, and How They are Co-Related with Correlation and Independence

2020 ◽  
Author(s):  
Timothy Falcon Crack
Keyword(s):  
Bivariate Normality

scholarly journals Testing Bivariate Normality Based on Nonlinear Canonical Analysis

2014 ◽  
Vol 3 (4) ◽  
Author(s):  
Mouhamed Amine Niang ◽  
Guy Martial Nkiet ◽  
Aliou Diop
Keyword(s):  
Canonical Analysis ◽  
Bivariate Normality

A test for bivariate normality with applications in microeconometric models

2013 ◽  
Vol 22 (4) ◽  
pp. 535-572 ◽  
Author(s):  
Riccardo Lucchetti ◽  
Claudia Pigini
Keyword(s):  
Bivariate Normality

scholarly journals Bivariate Distributions Underlying Responses to Ordinal Variables

Psych ◽  
2021 ◽  
Vol 3 (4) ◽  
pp. 562-578
Author(s):  
Laura Kolbe ◽  
Frans Oort ◽  
Suzanne Jak
Keyword(s):  
Correlation Coefficient ◽  
Latent Variables ◽  
Ordinal Data ◽  
Bivariate Normal Distribution ◽  
Polychoric Correlation ◽  
Bivariate Distributions ◽  
Normal Distributions ◽  
Ordinal Variables ◽  
Bivariate Normal ◽  
Bivariate Normality

The association between two ordinal variables can be expressed with a polychoric correlation coefficient. This coefficient is conventionally based on the assumption that responses to ordinal variables are generated by two underlying continuous latent variables with a bivariate normal distribution. When the underlying bivariate normality assumption is violated, the estimated polychoric correlation coefficient may be biased. In such a case, we may consider other distributions. In this paper, we aimed to provide an illustration of fitting various bivariate distributions to empirical ordinal data and examining how estimates of the polychoric correlation may vary under different distributional assumptions. Results suggested that the bivariate normal and skew-normal distributions rarely hold in the empirical datasets. In contrast, mixtures of bivariate normal distributions were often not rejected.

A test for bivariate normality

1988 ◽  
Vol 6 (6) ◽  
pp. 407-412 ◽  
Author(s):  
D.J. Best ◽  
J.C.W. Rayner
Keyword(s):  
Bivariate Normality

Logistics Performance Index: Methodological Issues

2020 ◽  
Vol 55 (4) ◽  
pp. 466-477
Author(s):  
Satyendra Nath Chakrabartty
Keyword(s):  
Performance Index ◽  
Geometric Mean ◽  
Principal Component ◽  
Point Of View ◽  
Geometric Means ◽  
Jel Codes ◽  
Critical Areas ◽  
Logistics Performance Index ◽  
Bivariate Normality ◽  
Underlying Variable

This article addresses limitations of Logistics Performance Index (LPI) and suggests remedies. Reliability of the instrument used in LPI may be better found by Angular Association method or Bhattacharyya’s measure, using only the frequencies or probabilities of item–response categories without involving assumptions of continuous nature or linearity or normality for the observed variables or the underlying variable being measured. The suggested methods also avoid test of uni-dimensionality, assumption of normality, bivariate normality. The problems of outlying observations and linear assumptions in principal component analysis for finding reliability theta are also avoided in each proposed method. Geometric mean approach provides a better alternative to compute LPI scores avoiding scaling and calculation of weights satisfies many desired properties and reduces level of substitutability between components, facilitates statistical test of equality of two geometric means and identifies critical areas for corrective measures. Such identifications are important from a policy point of view. The graph of LPI for a country over a long period of time reflects pattern of growth of LPI for the country. The method helps to rank and benchmark the countries, if the target vector is taken as LPI score of the best performing country. JEL Codes: C43, C54

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