Some partial ordering results on record values

1990 ◽  
Vol 19 (1) ◽  
pp. 299-306 ◽  
Author(s):  
Subhash C. Kochar
2019 ◽  
Vol 5 (1) ◽  
Author(s):  
Joshua Banks Mailman

Milton Babbitt has been a controversial and iconic figure, which has indirectly led to fallacious assumptions about how his music is made, and therefore to fundamental misconceptions about how it might be heard and appreciated. This video (the first of a three-part video essay) reconsiders his music in light of both his personal traits and a more precise examination of the constraints and freedoms entailed by his unusual and often misunderstood compositional practices, which are based inherently on partial ordering (as well as pitch repetition), which enables a surprising amount of freedom to compose the surface details we hear. The opening of Babbitt’s Composition for Four Instruments (1948) and three recompositions (based on re-ordering of pitches) demonstrate the freedoms intrinsic to partial ordering.


1983 ◽  
Vol 20 (03) ◽  
pp. 529-536
Author(s):  
W. J. R. Eplett

A natural requirement to impose upon the life distribution of a component is that after inspection at some randomly chosen time to check whether it is still functioning, its life distribution from the time of checking should be bounded below by some specified distribution which may be defined by external considerations. Furthermore, the life distribution should ideally be minimal in the partial ordering obtained from the conditional probabilities. We prove that these specifications provide an apparently new characterization of the DFRA class of life distributions with a corresponding result for IFRA distributions. These results may be transferred, using Slepian's lemma, to obtain bounds for the boundary crossing probabilities of a stationary Gaussian process.


2021 ◽  
Vol 13 (11) ◽  
pp. 6278
Author(s):  
Lars Carlsen ◽  
Rainer Bruggemann

The inequality within the 27 European member states has been studied. Six indicators proclaimed by Eurostat to be the main indicators charactere the countries: (i) the relative median at-risk-of-poverty gap, (ii) the income distribution, (iii) the income share of the bottom 40% of the population, (iv) the purchasing power adjusted GDP per capita, (v) the adjusted gross disposable income of households per capita and (vi) the asylum applications by state of procedure. The resulting multi-indicator system was analyzed applying partial ordering methodology, i.e., including all indicators simultaneously without any pretreatment. The degree of inequality was studied for the years 2010, 2015 and 2019. The EU member states were partially ordered and ranked. For all three years Luxembourg, The Netherlands, Austria, and Finland are found to be highly ranked, i.e., having rather low inequality. Bulgaria and Romania are, on the other hand, for all three years ranked low, with the highest degree of inequality. Excluding the asylum indicator, the risk-poverty-gap and the adjusted gross disposable income were found as the most important indicators. If, however, the asylum application is included, this indicator turns out as the most important for the mutual ranking of the countries. A set of additional indicators was studied disclosing the educational aspect as of major importance to achieve equality. Special partial ordering tools were applied to study the role of the single indicators, e.g., in relation to elucidate the incomparability of some countries to all other countries within the union.


2020 ◽  
Vol 8 (1) ◽  
pp. 22-35
Author(s):  
M. Shakil ◽  
M. Ahsanullah

AbstractThe objective of this paper is to characterize the distribution of the condition number of a complex Gaussian matrix. Several new distributional properties of the distribution of the condition number of a complex Gaussian matrix are given. Based on such distributional properties, some characterizations of the distribution are given by truncated moment, order statistics and upper record values.


2020 ◽  
Vol 70 (6) ◽  
pp. 1457-1468
Author(s):  
Haroon M. Barakat ◽  
M. H. Harpy

AbstractIn this paper, we investigate the asymptotic behavior of the multivariate record values by using the Reduced Ordering Principle (R-ordering). Necessary and sufficient conditions for weak convergence of the multivariate record values based on sup-norm are determined. Some illustrative examples are given.


2020 ◽  
Vol 72 (2) ◽  
pp. 89-110
Author(s):  
Manoj Chacko ◽  
Shiny Mathew

In this article, the estimation of [Formula: see text] is considered when [Formula: see text] and [Formula: see text] are two independent generalized Pareto distributions. The maximum likelihood estimators and Bayes estimators of [Formula: see text] are obtained based on record values. The Asymptotic distributions are also obtained together with the corresponding confidence interval of [Formula: see text]. AMS 2000 subject classification: 90B25


Author(s):  
Peihan Xiong ◽  
Weiwei Zhuang ◽  
Guoxin Qiu
Keyword(s):  

1968 ◽  
Vol 9 (1) ◽  
pp. 46-66 ◽  
Author(s):  
W. D. Munn

Let S be a semigroup whose set E of idempotents is non-empty. We define a partial ordering ≧ on E by the rule that e ≧ f and only if ef = f = fe. If E = {ei: i∈ N}, where N denotes the set of all non-negative integers, and if the elements of E form the chainthen S is called an ω-semigroup.


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