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2016•Unpublished venueRequires access

THE LAW OF THE ITERATED LOGARITHM FOR EMPIRICAL DISTRIBUTIONS

Helen Finkelstein

Open publisher page 8 citations

Abstract

A law of the iterated logarithm is derived for the empirical distribution functions of a sequence of independent identically distributed random variables. Convergence is in the uniform topology on the space of functions on the reals with discontinuities of the first kind only. The proof depends on a law of the iterated logarithm for independent identically distributed vector-valued random variables.

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What this paper is about

A law of the iterated logarithm is derived for the empirical distribution functions of a sequence of independent identically distributed random variables. Convergence is in the uniform topology on the space of functions on the reals with discontinuities of the first kind only. The proof depends on a law of the iterated logarithm for independent identically distributed vector-valued random variables.

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OpenAlex reports 8 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

A law of the iterated logarithm is derived for the empirical distribution functions of a sequence of independent identically distributed random variables. Convergence is in the uniform topology on the space of functions on the reals with discontinuities of the first kind only. The proof depends on a law of the iterated logarithm for independent identically distributed vector-valued random variables.

Key concepts: Law of the iterated logarithm, Iterated logarithm, Independent and identically distributed random variables, Mathematics, Logarithm, Random variable, Sequence (biology), Central limit theorem

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