scholarly journals Three kinds of discrete approximations of statistical multivariate distributions and their applications

2021 ◽  
pp. 104829
Author(s):  
Jun Yang ◽  
Ping He ◽  
Kai-Tai Fang
Keyword(s):  
Discrete Approximations ◽  
Multivariate Distributions

scholarly journals Non-local Solvable Birth–Death Processes

2021 ◽  
Author(s):  
Giacomo Ascione ◽  
Nikolai Leonenko ◽  
Enrica Pirozzi
Keyword(s):  
Differential Equations ◽  
Orthogonal Polynomials ◽  
Limit Distribution ◽  
Spectral Decomposition ◽  
Strong Solutions ◽  
Stochastic Representation ◽  
Discrete Approximations ◽  
Local Difference ◽  
Non Local ◽  
Birth Death

AbstractIn this paper, we study strong solutions of some non-local difference–differential equations linked to a class of birth–death processes arising as discrete approximations of Pearson diffusions by means of a spectral decomposition in terms of orthogonal polynomials and eigenfunctions of some non-local derivatives. Moreover, we give a stochastic representation of such solutions in terms of time-changed birth–death processes and study their invariant and their limit distribution. Finally, we describe the correlation structure of the aforementioned time-changed birth–death processes.

Multivariate distributions of order κ

1988 ◽  
Vol 7 (3) ◽  
pp. 207-216 ◽  
Author(s):  
Andreas N. Philippou ◽  
Demetris L. Antzoulakos ◽  
Gregory A. Tripsiannis
Keyword(s):  
Multivariate Distributions

Testing multivariate distributions in GARCH models

2008 ◽  
Vol 143 (1) ◽  
pp. 19-36 ◽  
Author(s):  
Jushan Bai ◽  
Zhihong Chen
Keyword(s):  
Garch Models ◽  
Multivariate Distributions

scholarly journals Cumulants of Multivariate Symmetric and Skew Symmetric Distributions

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1383
Author(s):  
Sreenivasa Rao Jammalamadaka ◽  
Emanuele Taufer ◽  
Gyorgy H. Terdik
Keyword(s):  
Comprehensive Treatment ◽  
Multivariate Distributions ◽  
Symmetric Distributions ◽  
Multivariate T Distribution ◽  
T Distribution ◽  
Multivariate T

This paper provides a systematic and comprehensive treatment for obtaining general expressions of any order, for the moments and cumulants of spherically and elliptically symmetric multivariate distributions; results for the case of multivariate t-distribution and related skew-t distribution are discussed in some detail.

scholarly journals Multivariate fractional phase–type distributions

2020 ◽  
Vol 23 (5) ◽  
pp. 1431-1451 ◽  
Author(s):  
Hansjörg Albrecher ◽  
Martin Bladt ◽  
Mogens Bladt
Keyword(s):  
Tail Dependence ◽  
Jump Process ◽  
Multivariate Distributions ◽  
New Class ◽  
Natural Time ◽  
Special Cases ◽  
Phase Type ◽  
Phase Type Distributions ◽  
Markovian Jump Process ◽  
Heavy Tailed

Abstract We extend the Kulkarni class of multivariate phase–type distributions in a natural time–fractional way to construct a new class of multivariate distributions with heavy-tailed Mittag-Leffler(ML)-distributed marginals. The approach relies on assigning rewards to a non–Markovian jump process with ML sojourn times. This new class complements an earlier multivariate ML construction [2] and in contrast to the former also allows for tail dependence. We derive properties and characterizations of this class, and work out some special cases that lead to explicit density representations.

Multivariate Distributions

2019 ◽  
pp. 107-166
Author(s):  
Wolfgang Karl Härdle ◽  
Léopold Simar
Keyword(s):  
Multivariate Distributions
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