scholarly journals Marginal Distributions of Random Vectors Generated by Affine Transformations of Independent Two-Piece Normal Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Maximiano Pinheiro
Keyword(s):  
Probability Density ◽  
Distribution Functions ◽  
Joint Density ◽  
Cumulative Distribution ◽  
Marginal Probability ◽  
Affine Transformations ◽  
Skewed Distributions ◽  
Random Vectors ◽  
Marginal Distributions ◽  
Cumulative Distribution Functions

Marginal probability density and cumulative distribution functions are presented for multidimensional variables defined by nonsingular affine transformations of vectors of independent two-piece normal variables, the most important subclass of Ferreira and Steel's general multivariate skewed distributions. The marginal functions are obtained by first expressing the joint density as a mixture of Arellano-Valle and Azzalini's unified skew-normal densities and then using the property of closure under marginalization of the latter class.

scholarly journals Cylcop: An R Package for Circular-Linear Copulae with Angular Symmetry

2021 ◽  
Author(s):  
Florian H. Hodel ◽  
John R. Fieberg
Keyword(s):  
Probability Density ◽  
Discrete Time ◽  
Random Variables ◽  
R Package ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Animal Movements ◽  
Cumulative Distribution Functions ◽  
Model Animal

The cylcop package extends the copula package to allow modeling of correlated circular-linear random variables using copulae that are symmetric in the circular dimension. We present and derive several new circular-linear copulae with this property and demonstrate how they can be implemented in the cylcop package to model animal movements in discrete time. The package contains methods for estimating copulae parameters, plotting probability density and cumulative distribution functions, and simulating data.

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