On a multivariate generalization of the covariance

2016 ◽  
Vol 46 (9) ◽  
pp. 4660-4669 ◽  
Author(s):  
Walter Díaz ◽  
Carles M. Cuadras
Keyword(s):  
Multivariate Generalization

The problem of variation

2021 ◽  
pp. 111-134
Author(s):  
Arlin Stoltzfus
Keyword(s):  
Quantitative Genetics ◽  
Raw Materials ◽  
Substantive Theory ◽  
Theory Of Evolution ◽  
Multivariate Generalization ◽  
Theory Of Variation ◽  
Broad Framework ◽  
The Moment ◽  
Evo Devo

Chapter 7 maps out a broad framework for considering the problem of variation in evolution. Under the neo-Darwinian view that variation merely plays the role of supplying random infinitesimal raw materials, with no dispositional influence on the course of evolution, a substantive theory of form and its variation is not required to specify a complete theory of evolution. This view has been breaking down from the moment it was proposed, and is now seriously challenged by results from evo-devo, comparative genomics, molecular evolution, and quantitative genetics. For instance, the multivariate generalization of quantitative genetics indicates that selection cannot possibly act as an independent governing force. Replacing a theory of variation as fuel with a theory of variation as a dispositional factor will require, at minimum, an understanding of tendencies of variation (source laws), and an understanding of how those tendencies affect evolution (consequence laws).

CLASSIFICATION OF MULTIVARIATE LIFE DISTRIBUTIONS BASED ON PARTIAL ORDERING

2002 ◽  
Vol 16 (1) ◽  
pp. 129-137 ◽  
Author(s):  
Dilip Roy
Keyword(s):  
Present Article ◽  
Failure Rate ◽  
Partial Ordering ◽  
Increasing Failure Rate ◽  
Multivariate Generalization ◽  
Partial Orderings ◽  
Life Distributions ◽  
New Better Than Used ◽  
Better Than

Barlow and Proschan presented some interesting connections between univariate classifications of life distributions and partial orderings where equivalent definitions for increasing failure rate (IFR), increasing failure rate average (IFRA), and new better than used (NBU) classes were given in terms of convex, star-shaped, and superadditive orderings. Some related results are given by Ross and Shaked and Shanthikumar. The introduction of a multivariate generalization of partial orderings is the object of the present article. Based on that concept of multivariate partial orderings, we also propose multivariate classifications of life distributions and present a study on more IFR-ness.

Multivariate Lomax distribution: properties and usefulness in reliability theory

1987 ◽  
Vol 24 (01) ◽  
pp. 170-177 ◽  
Author(s):  
Tapan Kumar Nayak
Keyword(s):  
Reliability Theory ◽  
Multivariate Distributions ◽  
Common Environment ◽  
Lomax Distribution ◽  
Multivariate Generalization ◽  
Multivariate Lomax Distribution

A model incorporating the effect of a common environment on several components (structurally independent) of a system is developed. A multivariate generalization of the Lomax (Pareto type 2) distribution is obtained by mixing exponential variables. Its relationship to other multivariate distributions is discussed. Several properties of this distribution are reported and their usefulness in reliability theory indicated. Finally, a further generalization of this multivariate Lomax distribution is presented.

On Wilks's Multivariate Generalization of the Correlation Ratio

Biometrika ◽  
1976 ◽  
Vol 63 (1) ◽  
pp. 59
Author(s):  
M. L. Hart ◽  
A. H. Money
Keyword(s):  
Correlation Ratio ◽  
Multivariate Generalization

scholarly journals Minimal factorizations of a cycle: a multivariate generating function

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Philippe Biane ◽  
Matthieu Josuat-Vergès
Keyword(s):  
Symmetric Group ◽  
Generating Function ◽  
Simple Formula ◽  
Hook Length ◽  
Noncrossing Partitions ◽  
Long Cycle ◽  
Number Of Factors ◽  
Multivariate Generalization ◽  
International Audience

International audience It is known that the number of minimal factorizations of the long cycle in the symmetric group into a product of k cycles of given lengths has a very simple formula: it is nk−1 where n is the rank of the underlying symmetric group and k is the number of factors. In particular, this is nn−2 for transposition factorizations. The goal of this work is to prove a multivariate generalization of this result. As a byproduct, we get a multivariate analog of Postnikov's hook length formula for trees, and a refined enumeration of final chains of noncrossing partitions.

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