Displaying similar documents to “The limiting distributions of the multinomial distribution”

Normalizing constants for a statistic based on logarithms of disjoint m-spacings

Franciszek Czekała (1996)

Applicationes Mathematicae

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The paper is concerned with the asymptotic normality of a certain statistic based on the logarithms of disjoint m-spacings. The exact and asymptotic mean and variance are computed in the case of uniform distribution on the interval [0,1]. This result is generalized to the case when the sample is drawn from a distribution with positive step density on [0,1].

The distribution of the sum-of-digits function

Michael Drmota, Johannes Gajdosik (1998)

Journal de théorie des nombres de Bordeaux

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By using a generating function approach it is shown that the sum-of-digits function (related to specific finite and infinite linear recurrences) satisfies a central limit theorem. Additionally a local limit theorem is derived.

On mean central limit theorems for stationary sequences

Jérôme Dedecker, Emmanuel Rio (2008)

Annales de l'I.H.P. Probabilités et statistiques

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In this paper, we give estimates of the minimal 𝕃 1 distance between the distribution of the normalized partial sum and the limiting gaussian distribution for stationary sequences satisfying projective criteria in the style of Gordin or weak dependence conditions.

Large deviations for Riesz potentials of additive processes

Richard Bass, Xia Chen, Jay Rosen (2009)

Annales de l'I.H.P. Probabilités et statistiques

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We study functionals of the form = ⋯ | ( )+⋯+ ( )| d  ⋯ d , where (), …, () are i.i.d. -dimensional symmetric stable processes of index 0<≤2. We obtain results about the large deviations and laws of the iterated logarithm for .