Characterization of discrete distributions using expected values

1995 ◽  
Vol 36 (1) ◽  
Author(s):  
J. M. Ruiz ◽  
J. Navarro
Keyword(s):  
Discrete Distributions ◽  
Expected Values

scholarly journals Predecessors and Successors in Random Mappings with Exchangeable In-Degrees

2013 ◽  
Vol 50 (3) ◽  
pp. 721-740 ◽  
Author(s):  
Jennie C. Hansen ◽  
Jerzy Jaworski
Keyword(s):  
Asymptotic Behaviour ◽  
Preferential Attachment ◽  
Degree Sequence ◽  
Discrete Distributions ◽  
Threshold Behaviour ◽  
Mapping Model ◽  
Random Mapping ◽  
Exact Distributions ◽  
Random Mappings ◽  
Expected Values

In this paper we characterise the distributions of the number of predecessors and of the number of successors of a given set of vertices, A, in the random mapping model, TnD̂ (see Hansen and Jaworski (2008)), with exchangeable in-degree sequence (D̂1,D̂2,…,D̂n). We show that the exact formulae for these distributions and their expected values can be given in terms of the distributions of simple functions of the in-degree variables D̂1,D̂2,…,D̂n. As an application of these results, we consider two special examples of TnD̂ which correspond to random mappings with preferential and anti-preferential attachment, and determine the exact distributions for the number of predecessors and the number of successors in these cases. We also characterise, for these two special examples, the asymptotic behaviour of the expected numbers of predecessors and successors and interpret these results in terms of the threshold behaviour of epidemic processes on random mapping graphs. The families of discrete distributions obtained in this paper are also of independent interest.

Optimal couplings are totally positive and more

2004 ◽  
Vol 41 (A) ◽  
pp. 321-332 ◽  
Author(s):  
Paul Glasserman ◽  
David D. Yao
Keyword(s):  
Transportation Problem ◽  
Random Variables ◽  
Total Positivity ◽  
Bivariate Distribution ◽  
Discrete Distributions ◽  
Optimal Solutions ◽  
Totally Positive ◽  
Maximal Correlation ◽  
Optimal Coupling

An optimal coupling is a bivariate distribution with specified marginals achieving maximal correlation. We show that optimal couplings are totally positive and, in fact, satisfy a strictly stronger condition we call the nonintersection property. For discrete distributions we illustrate the equivalence between optimal coupling and a certain transportation problem. Specifically, the optimal solutions of greedily-solvable transportation problems are totally positive, and even nonintersecting, through a rearrangement of matrix entries that results in a Monge sequence. In coupling continuous random variables or random vectors, we exploit a characterization of optimal couplings in terms of subgradients of a closed convex function to establish a generalization of the nonintersection property. We argue that nonintersection is not only stronger than total positivity, it is the more natural concept for the singular distributions that arise in coupling continuous random variables.

Characterization of Spanish grapevine cultivar diversity using sequence-tagged microsatellite site markers

Genome ◽  
2003 ◽  
Vol 46 (1) ◽  
pp. 10-18 ◽  
Author(s):  
J P Martín ◽  
J Borrego ◽  
F Cabello ◽  
J M Ortiz
Keyword(s):  
Plant Material ◽  
Vitis Vinifera L ◽  
Germplasm Bank ◽  
Discrimination Power ◽  
Grapevine Cultivar ◽  
Genotype Identification ◽  
Site Markers ◽  
Expected Values ◽  
Cultivar Diversity

A broad germplasm bank collection containing most of the autochthonous Spanish grapevine cultivars was analyzed using six sequence-tagged microsatellite site (STMS) loci: VVS2, VVMD5, VVMD7, ssrVrZAG47, ssrVrZAG62, and ssrVrZAG79. The number of alleles obtained ranged from 9 in ssrVrZAG47 to 13 in VVS2, and the observed genotypes per locus varied between 24 (ssrVrZAG47) and 41 (VVSS2). A total of 57 unique genotypes were obtained considering all 6 loci, and 40 varieties presented at least 1 of these specific genotypes. The genotypic combinations for the 6 loci have generated 163 different profiles in the 176 cultivars. Ten pairs of accessions and one group of four Garnacha's cultivars can not be differentiated. The observed heterozygosity varied between 75.6 (VVMD7) and 90.9% (VVMD5), without significant differences from the expected values for any loci. The VVMD5 locus was the most informative, and also showed the highest discrimination power. The cumulative discrimination power for all six loci was practically 1; however, in fact, these STMS loci have differentiated only about 93% of the accessions, probably owing to high relatedness of the plant material. Usefulness of this STMS set for characterization of a Spanish grapevine collection is emphasized, as well as the elaboration of databases with these molecular markers.Key words: Vitis vinifera L., STMS markers, genotype identification, grapevine synonymies, germplasm bank.

Optimal couplings are totally positive and more

2004 ◽  
Vol 41 (A) ◽  
pp. 321-332
Author(s):  
Paul Glasserman ◽  
David D. Yao
Keyword(s):  
Transportation Problem ◽  
Random Variables ◽  
Total Positivity ◽  
Bivariate Distribution ◽  
Discrete Distributions ◽  
Optimal Solutions ◽  
Totally Positive ◽  
Maximal Correlation ◽  
Optimal Coupling

An optimal coupling is a bivariate distribution with specified marginals achieving maximal correlation. We show that optimal couplings are totally positive and, in fact, satisfy a strictly stronger condition we call the nonintersection property. For discrete distributions we illustrate the equivalence between optimal coupling and a certain transportation problem. Specifically, the optimal solutions of greedily-solvable transportation problems are totally positive, and even nonintersecting, through a rearrangement of matrix entries that results in a Monge sequence. In coupling continuous random variables or random vectors, we exploit a characterization of optimal couplings in terms of subgradients of a closed convex function to establish a generalization of the nonintersection property. We argue that nonintersection is not only stronger than total positivity, it is the more natural concept for the singular distributions that arise in coupling continuous random variables.

scholarly journals Reliability Characterization of Binary-Imaged Multi-State Coherent Threshold Systems

2020 ◽  
Vol 6 (1) ◽  
pp. 309-321
Author(s):  
Ali Muhammad Ali Rushdi ◽  
Fares Ahmad Muhammad Ghaleb
Keyword(s):  
System Structure ◽  
System Failure ◽  
Weighted Sum ◽  
Zero Level ◽  
Algebraic Expressions ◽  
Sum Of Products ◽  
Expected Values ◽  
System Success ◽  
Karnaugh Map

A notable reliability model is the binary threshold system (also called the weighted-k-out-of-n system), which is a dichotomous system that is successful if and only if the weighted sum of its component successes exceeds or equals a particular threshold. The aim of this paper is to extend the utility of this model to the reliability analysis of a homogeneous binary-imaged multi-state coherent threshold system of (m+1) states, which is a non-repairable system with independent non-identical components. The paper characterizes such a system via switching-algebraic expressions of either system success or system failure at each non-zero level. These expressions are given either (a) as minimal sum-of-products formulas, or (b) as probability–ready expressions, which can be immediately converted, on a one-to-one basis, into probabilities or expected values. The various algebraic characterizations can be supplemented by a multitude of map representations, including a single multi-value Karnaugh map (MVKM) (giving a superfluous representation of the system structure function S), (m+1) maps of binary entries and multi-valued inputs representing the binary instances of S, or m maps, again of binary entries and multi-valued inputs, but now representing the success/failure at every non-zero level of the system. We demonstrate how to reduce these latter maps to conventional Karnaugh maps (CKMs) of much smaller sizes. Various characterizations are inter-related, and also related to pertinent concepts such as shellability of threshold systems, and also to characterizations via minimal upper vectors or via maximal lower vectors.

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