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Bounds in poisson approximation for random sums of Bernoulli random variables

Let X[subscript n] be a sequence of Bernoulli random variables and a positive integer-valued random variable. Define S[subscript N] = X₁ +X₂ +… X [subscript n]) be random sums. Assume N, X₁, X₂, … are independent. In this thesis, we establish uniform and non-uniform bounds in Poisson approximation for S[subscript N]
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Zero-inflated Poisson regression, with an application to defects in manufacturing

, 1992
D. Lambert
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q-deformed Poisson random variables on q-Fock space

, 2000
Naoko Saitoh, Hiroaki Yoshida
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Equations for probability density of response of dynamic systems to a class of non-Poisson random impulse process excitations

, 2008
R. Iwankiewicz
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Regression analyses of counts and rates: Poisson, overdispersed Poisson, and negative binomial models.

Psychological bulletin, 1995
W. Gardner, E. Mulvey, Esther C. Shaw
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The Kumaraswamy Poisson-G Family of Distribution: Its Properties and Applications

, 2020
S. Chakraborty, Laba Handique, F. Jamal
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Zero‐Inflated Poisson and Binomial Regression with Random Effects: A Case Study

Biometrics, 2000
D. Hall
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