Three limit theorems for vacancy in multivariate coverage problems

Peter Hall

Journal of Multivariate Analysis, 1985, vol. 16, issue 2, 211-236

Abstract: Three limit theorems describing asymptotic distribution of vacancy in general multivariate coverage problems are proved, in which n k-dimensional spheres are distributed within a k-dimensional unit cube according to a density f. The first result (a central limit theorem) describes the case where the proportion of vacancy converges to a fixed constant lying between 0 and 1. The last two results treat the case where the proportion of vacancy tends to 1 as n --> [infinity]. Results of this nature have hitherto been available only for restricted k and/or for f equal to the uniform density.

Keywords: central; limit; theorem; compound; Poisson; distribution; geometric; probability; vacancy (search for similar items in EconPapers)
Date: 1985
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