Suggested by experiments concerning photons statistics, we study two kinds of problems: firstly, we give a complete characterization of the distributions for random sums of i.i.d. Bernoulli variables sharing a suitable stability property. Next, we study the distribution of a multivariate generalization of the univariate random sums and we obtain the explicit distribution of their L1 norm in terms of Bernstein polynomials.
Characterization and stability of light statistics distributions
CASINI, EMANUELE GIUSEPPE;MARTINELLI, ANDREA
2013-01-01
Abstract
Suggested by experiments concerning photons statistics, we study two kinds of problems: firstly, we give a complete characterization of the distributions for random sums of i.i.d. Bernoulli variables sharing a suitable stability property. Next, we study the distribution of a multivariate generalization of the univariate random sums and we obtain the explicit distribution of their L1 norm in terms of Bernstein polynomials.
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