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The paper presents inequalities between four descriptive statistics that can be expressed in the form [P − E(P)]/[1 − E(P)], where P is the observed proportion of agreement of a k × k table with identical categories, and E(P) is a function of the marginal probabilities. Scott’s π is an upper bound of Goodman and Kruskal’s λ and a lower bound of both Bennett et al. S and Cohen’s κ. We introduce a concept for the marginal probabilities of the k×k table called weak marginal symmetry. Using the rearrangement inequality, it is shown that Bennett et al. S is an upper bound of Cohen’s κ if the k×k table is weakly marginal symmetric.

Let Xl, · ··, Χ n be independent binary variables with parameters θl, · ··, θ n respectively, and let R denote the length of the longest run of 1's. This note concerns a new expression for and a rearrangement inequality. The inequality is applied to solve an optimal permutation problem for consecutive-k-out-of-n: F networks, and its implications on a recent conjecture of Derman et al. (1982) are discussed.

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Inequalities Between Kappa and Kappa-Like Statistics for k × k Tables

A rearrangement inequality for the longest run, with an application to network reliability

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2 results

Inequalities Between Kappa and Kappa-Like Statistics for k × k Tables

A rearrangement inequality for the longest run, with an application to network reliability