scholarly journals Cumulants and partition lattices III: Multiply-indexed arrays

1986 ◽  
Vol 40 (2) ◽  
pp. 161-182 ◽  
Author(s):  
T. P. Speed
Keyword(s):  
Random Variables ◽  
Unbiased Estimation ◽  
Linear Combinations ◽  
Components Of Variance ◽  
Partition Lattices ◽  
Special Case

AbstractEarlier work of the author exploiting the role of partition lattices and their Mbius functions in the theory of cumulants, k-statistics and their generalisations is extended to multiply-indexed arrays of random variables. The natural generalisations of cumulants and k-statistics to this context are shown to include components of variance and the associated linear combinations of mean-squares which are used to estimate them. Expressions for the generalised cumulants of arrays built up as sums of independent arrays of effects as in anova models are derived in terms of the generalized cumulants of the effects. The special case of degree two, covering the unbiased estimation of components of variance, is discussed in some detail.

scholarly journals Cumulants and Partition Lattices V. Calculating Generalized k-Statistics

1988 ◽  
Vol 44 (2) ◽  
pp. 171-196 ◽  
Author(s):  
T. P. Speed ◽  
H. L. Silcock
Keyword(s):  
Variance Component ◽  
Random Variables ◽  
Component Analysis ◽  
Variance Component Analysis ◽  
Components Of Variance ◽  
Partition Lattices

AbstractA method is developed for obtaining compact, easily computed and statistically interpretable expressions for the generalized k-statistics associated with multiply-indexed arrays of random variables such as those which arise in variance component analysis. These expressions will be used in the next paper in this series to give formulae for variances and covariances of estimates of components of variance.

scholarly journals Some inequalities of linear combinations of independent random variables: II

Bernoulli ◽  
2013 ◽  
Vol 19 (5A) ◽  
pp. 1776-1789 ◽  
Author(s):  
Xiaoqing Pan ◽  
Maochao Xu ◽  
Taizhong Hu
Keyword(s):  
Random Variables ◽  
Independent Random Variables ◽  
Linear Combinations

On improvements of the order of approximation in the Poisson limit theorem

1996 ◽  
Vol 33 (01) ◽  
pp. 146-155 ◽  
Author(s):  
K. Borovkov ◽  
D. Pfeifer
Keyword(s):  
Limit Theorem ◽  
Random Variables ◽  
Poisson Approximation ◽  
Order Of Approximation ◽  
Operator Semigroups ◽  
Bernoulli Random Variables ◽  
Usual Rate ◽  
Poisson Limit ◽  
Poisson Measures ◽  
Special Case

In this paper we consider improvements in the rate of approximation for the distribution of sums of independent Bernoulli random variables via convolutions of Poisson measures with signed measures of specific type. As a special case, the distribution of the number of records in an i.i.d. sequence of length n is investigated. For this particular example, it is shown that the usual rate of Poisson approximation of O(1/log n) can be lowered to O(1/n 2). The general case is discussed in terms of operator semigroups.

scholarly journals Academic policy advice in consensus-seeking countries: the cases of Belgium and Germany

2019 ◽  
pp. 002085231987878 ◽  
Author(s):  
Valérie Pattyn ◽  
Sonja Blum ◽  
Ellen Fobé ◽  
Mirjam Pekar-Milicevic ◽  
Marleen Brans
Keyword(s):  
Academic Research ◽  
Policy Advice ◽  
Current Evidence ◽  
Common Trends ◽  
Policy Advisory Systems ◽  
Academic Policy ◽  
Advisory Systems ◽  
The Government ◽  
Special Case

Research on policy-advisory systems worldwide has shown that historically dominant sources of advice traditionally located in-house to the government have been increasingly supplemented by other actors and outside knowledge. However, the vast majority of research has concentrated on the anglophone context. Yet, countries with a consensus-seeking, neo-corporatist tradition provide a special case in terms of policy advice and merit more scholarly attention. What counts as evidence in these countries is the expert rationality of institutional representatives. The position and role of academic research in consensus-based systems is unclear, and is the focus of this article. Can we observe commonalities across consensus-style countries, or do differences prevail? We investigate two typical consensus-seeking countries: Belgium and Germany. To examine the supply side of policy advice, the article reviews current evidence regarding their policy-advisory systems. For the demand side, we present insights from a survey among federal ministerial officials. We find common trends between the two cases but their nature and extent are idiosyncratic. In Belgium, the supply of and demand for academic policy advice is comparatively lower, while the German case exhibits more change in the advisory landscape and institutionalisation of the supply of and demand for academic research. Points for practitioners   • Countries with a consensus-seeking, neo-corporatist tradition provide a special case in terms of policy advice.   • The findings suggest that there are common trends but their nature and extent are idiosyncratic.   • In Belgium, the supply of and demand for academic advice is comparatively lower.   • Germany’s policy-advisory landscape exhibits more change and institutionalisation of the supply of and demand for academic research.

scholarly journals RATIONAL LOCAL SYSTEMS AND CONNECTED FINITE LOOP SPACES

2021 ◽  
pp. 1-29
Author(s):  
DREW HEARD
Keyword(s):  
Lie Group ◽  
Loop Space ◽  
Algebraic Model ◽  
Compact Lie Group ◽  
Loop Spaces ◽  
Local Systems ◽  
Special Case ◽  
Finite Loop ◽  
Finite Loop Space

Abstract Greenlees has conjectured that the rational stable equivariant homotopy category of a compact Lie group always has an algebraic model. Based on this idea, we show that the category of rational local systems on a connected finite loop space always has a simple algebraic model. When the loop space arises from a connected compact Lie group, this recovers a special case of a result of Pol and Williamson about rational cofree G-spectra. More generally, we show that if K is a closed subgroup of a compact Lie group G such that the Weyl group W G K is connected, then a certain category of rational G-spectra “at K” has an algebraic model. For example, when K is the trivial group, this is just the category of rational cofree G-spectra, and this recovers the aforementioned result. Throughout, we pay careful attention to the role of torsion and complete categories.

scholarly journals Response to governmental COVID-19 restrictions: the role of informal institutions

2021 ◽  
pp. 1-17
Author(s):  
Katarzyna Bentkowska
Keyword(s):  
Social Relations ◽  
Informal Institutions ◽  
Special Case ◽  
Formal Rules

Abstract This paper explains how informal institutions influence the reaction to the COVID-19 pandemic and the response to formal restrictions. I claim that it is not enough to introduce countermeasures, as individuals must follow them if they are to be effective. The acceptance of such measures is reflected in individuals' degrees of mobility decrease and contact reduction, the aims of governmental restrictions. I identify a group of attitudes connected with individuals' responses that differ across countries. They are associated with social relations and approaches to dealing with problems. The analysis confirms that formal restrictions can be seen as successful only if they are supported by strong informal institutions. In some cases, they even define individuals' reactions more than formal recommendations. The findings are useful not only for explaining the special case of reaction to pandemic restrictions but also for investigating what generally determines individuals' compliance with formal rules.

THE ROLE OF OXYGEN IN TISSUE MAINTENANCE: MATHEMATICAL MODELING AND QUALITATIVE ANALYSIS

2008 ◽  
Vol 18 (08) ◽  
pp. 1409-1441 ◽  
Author(s):  
AVNER FRIEDMAN ◽  
BEI HU
Keyword(s):  
Mathematical Modeling ◽  
Free Boundary ◽  
Qualitative Analysis ◽  
Phase I ◽  
Stationary Solution ◽  
Oxygen Concentration ◽  
Existence And Uniqueness ◽  
Symmetric Case ◽  
Special Case

The cells in a tissue occupying a region Ωt are divided according to their cycling phase. The density pi of cells in phase i depends on the spatial variable x, the time t, and the time si since the cells entered in phase i. The pi(x, t, si) and the oxygen concentration w(x, t) satisfy a system of PDEs in Ωt, and the boundary of Ωt is a free boundary. We denote by [Formula: see text] the oxygen concentration on the free boundary and consider the radially symmetric case, so that Ωt = {r < R(t)}. We prove that R(t) is always bounded; furthermore, if [Formula: see text] is small, then R(t) → 0 as t → ∞, and if [Formula: see text] is large, then R(t) ≥ c > 0 for all t. Finally, we prove the existence and uniqueness of a stationary solution in a special case.

scholarly journals SOME UNIFIED RESULTS ON COMPARING LINEAR COMBINATIONS OF INDEPENDENT GAMMA RANDOM VARIABLES

2012 ◽  
Vol 26 (3) ◽  
pp. 393-404 ◽  
Author(s):  
Subhash Kochar ◽  
Maochao Xu
Keyword(s):  
Random Variables ◽  
Stochastic Orders ◽  
Sufficient Condition ◽  
Linear Combinations

In this paper, a new sufficient condition for comparing linear combinations of independent gamma random variables according to star ordering is given. This unifies some of the newly proved results on this problem. Equivalent characterizations between various stochastic orders are established by utilizing the new condition. The main results in this paper generalize and unify several results in the literature including those of Amiri, Khaledi, and Samaniego [2], Zhao [18], and Kochar and Xu [9].

scholarly journals Improved bounds for the availability and unavailability in a fixed time interval for systems of maintained, interdependent components

1980 ◽  
Vol 12 (01) ◽  
pp. 200-221 ◽  
Author(s):  
B. Natvig
Keyword(s):  
Lower Bound ◽  
System Reliability ◽  
Nuclear Reactors ◽  
Random Variables ◽  
Fixed Time ◽  
Time Interval ◽  
Coherent System ◽  
Exact Results ◽  
Fixed Time Interval ◽  
Special Case

In this paper we arrive at a series of bounds for the availability and unavailability in the time interval I = [t A , t B ] ⊂ [0, ∞), for a coherent system of maintained, interdependent components. These generalize the minimal cut lower bound for the availability in [0, t] given in Esary and Proschan (1970) and also most bounds for the reliability at time t given in Bodin (1970) and Barlow and Proschan (1975). In the latter special case also some new improved bounds are given. The bounds arrived at are of great interest when trying to predict the performance process of the system. In particular, Lewis et al. (1978) have revealed the great need for adequate tools to treat the dependence between the random variables of interest when considering the safety of nuclear reactors. Satyanarayana and Prabhakar (1978) give a rapid algorithm for computing exact system reliability at time t. This can also be used in cases where some simpler assumptions on the dependence between the components are made. It seems, however, impossible to extend their approach to obtain exact results for the cases treated in the present paper.

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