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.

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 Branching-stable point measures and processes

2018 ◽  
Vol 50 (4) ◽  
pp. 1294-1314
Author(s):  
Jean Bertoin ◽  
Aser Cortines ◽  
Bastien Mallein
Keyword(s):  
Asymptotic Behavior ◽  
Classical Theory ◽  
Branching Processes ◽  
Random Variables ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Scaling Exponent ◽  
Stable Point ◽  
Cumulative Distribution Functions ◽  
Stable Random Variables

Abstract We introduce and study the class of branching-stable point measures, which can be seen as an analog of stable random variables when the branching mechanism for point measures replaces the usual addition. In contrast with the classical theory of stable (Lévy) processes, there exists a rich family of branching-stable point measures with a negative scaling exponent, which can be described as certain Crump‒Mode‒Jagers branching processes. We investigate the asymptotic behavior of their cumulative distribution functions, that is, the number of atoms in (-∞, x] as x→∞, and further depict the genealogical lineage of typical atoms. For both results, we rely crucially on the work of Biggins (1977), (1992).

scholarly journals A Note on the Central Limit Theorems for Dependent Random Variables

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Yilun Shang
Keyword(s):  
Central Limit ◽  
Limit Theorems ◽  
Random Variables ◽  
Distribution Functions ◽  
Central Limit Theorems ◽  
Cumulative Distribution ◽  
Characteristic Functions ◽  
Mixing Conditions ◽  
Cumulative Distribution Functions ◽  
Probability And Statistics

Classical central limit theorem is considered the heart of probability and statistics theory. Our interest in this paper is central limit theorems for functions of random variables under mixing conditions. We impose mixing conditions on the differences between the joint cumulative distribution functions and the product of the marginal cumulative distribution functions. By using characteristic functions, we obtain several limit theorems extending previous results.

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