scholarly journals The FKG Inequality and Some Monotonicity Properties of Partial Orders

1980 ◽  
Vol 1 (3) ◽  
pp. 295-299 ◽  
Author(s):  
L. A. Shepp
Keyword(s):  
Partial Orders ◽  
Fkg Inequality ◽  
Monotonicity Properties ◽  
The Fkg Inequality

scholarly journals LRU is better than FIFO under the independent reference model

1992 ◽  
Vol 29 (01) ◽  
pp. 239-243 ◽  
Author(s):  
J. van den Berg ◽  
A. Gandolfi
Keyword(s):  
Reference Model ◽  
Storage System ◽  
Replacement Strategy ◽  
Fkg Inequality ◽  
The Fkg Inequality ◽  
First In First Out ◽  
System Operating ◽  
Better Than

Consider a two-level storage system operating with the least recently used (LRU) or the first-in, first-out (FIFO) replacement strategy. Accesses to the main storage are described by the independent reference model (IRM). Using the FKG inequality, we prove that the miss ratio for LRU is smaller than or equal to the miss ratio for FIFO.

Multivariate monotone likelihood ratio and uniform conditional stochastic order

1982 ◽  
Vol 19 (3) ◽  
pp. 695-701 ◽  
Author(s):  
Ward Whitt
Keyword(s):  
Conditional Probability ◽  
Likelihood Ratio ◽  
Probability Distributions ◽  
Stochastic Order ◽  
Total Positivity ◽  
Probability Measures ◽  
Monotone Likelihood Ratio ◽  
Fkg Inequality ◽  
The Fkg Inequality

Karlin and Rinott (1980) introduced and investigated concepts of multivariate total positivity (TP2) and multivariate monotone likelihood ratio (MLR) for probability measures on Rn These TP and MLR concepts are intimately related to supermodularity as discussed in Topkis (1968), (1978) and the FKG inequality of Fortuin, Kasteleyn and Ginibre (1971). This note points out connections between these concepts and uniform conditional stochastic order (ucso) as defined in Whitt (1980). ucso holds for two probability distributions if there is ordinary stochastic order for the corresponding conditional probability distributions obtained by conditioning on subsets from a specified class. The appropriate subsets to condition on for ucso appear to be the sublattices of Rn. Then MLR implies ucso, with the two orderings being equivalent when at least one of the probability measures is TP2.

scholarly journals Negative Dependence Through the FKG Inequality

1996 ◽  
Vol 3 (27) ◽  
Author(s):  
Devdatt P. Dubhashi ◽  
Volker Priebe ◽  
Desh Ranjan
Keyword(s):  
Random Variables ◽  
Negative Association ◽  
Negative Dependence ◽  
Correlation Inequality ◽  
General Technique ◽  
Fkg Inequality ◽  
Binary Random Variables ◽  
The Fkg Inequality ◽  
Occupancy Problems ◽  
Special Case

We investigate random variables arising in occupancy problems, and show the variables to be negatively associated, that is, negatively dependent in a strong sense. Our proofs are based on the FKG correlation inequality, and they suggest a useful, general technique for proving negative dependence among random variables. We also show that in the special case of two binary random variables, the notions of negative correlation and negative association coincide.

On some percolation results of J. M. Hammersley

1979 ◽  
Vol 16 (03) ◽  
pp. 526-540 ◽  
Author(s):  
J. G. Oxley ◽  
D. J. A. Welsh
Keyword(s):  
Lower Bound ◽  
Upper Bound ◽  
Percolation Theory ◽  
Fkg Inequality ◽  
Percolation Probability ◽  
Finite Set ◽  
The Fkg Inequality ◽  
Arbitrary Graphs

We examine how much classical percolation theory on lattices can be extended to arbitrary graphs or even clutters of subsets of a finite set. In the process we get new short proofs of some theorems of J. M. Hammersley. The FKG inequality is used to get an upper bound for the percolation probability and we also derive a lower bound. In each case we characterise when these bounds are attained.

Multivariate monotone likelihood ratio and uniform conditional stochastic order

1982 ◽  
Vol 19 (03) ◽  
pp. 695-701 ◽  
Author(s):  
Ward Whitt
Keyword(s):  
Conditional Probability ◽  
Likelihood Ratio ◽  
Probability Distributions ◽  
Stochastic Order ◽  
Total Positivity ◽  
Probability Measures ◽  
Monotone Likelihood Ratio ◽  
Fkg Inequality ◽  
The Fkg Inequality

Karlin and Rinott (1980) introduced and investigated concepts of multivariate total positivity (TP2) and multivariate monotone likelihood ratio (MLR) for probability measures on Rn These TP and MLR concepts are intimately related to supermodularity as discussed in Topkis (1968), (1978) and the FKG inequality of Fortuin, Kasteleyn and Ginibre (1971). This note points out connections between these concepts and uniform conditional stochastic order (ucso) as defined in Whitt (1980). ucso holds for two probability distributions if there is ordinary stochastic order for the corresponding conditional probability distributions obtained by conditioning on subsets from a specified class. The appropriate subsets to condition on for ucso appear to be the sublattices of Rn . Then MLR implies ucso, with the two orderings being equivalent when at least one of the probability measures is TP2.

Some Monotonicity Properties of Partial Orders

1980 ◽  
Vol 1 (3) ◽  
pp. 251-258 ◽  
Author(s):  
R. L. Graham ◽  
A. C. Yao ◽  
F. F. Yao
Keyword(s):  
Partial Orders ◽  
Monotonicity Properties
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