Poisson approximation to the convolution of PSDs

• Autorzy: Kumar A. N. , Vellaisamy P. , Viens F.

Identyfikatory

DOI

10.37190/0208-4147.00056

• Języki publikacji: EN

Abstrakty

EN

In this article, we obtain, for the total variation distance, error bounds for Poisson approximation to the convolution of power series distributions via Stein's method. This provides a unified approach to many known discrete distributions. Several Poisson limit theorems follow as corollaries from our bounds. As applications, we compare Poisson approximation results with negative binomial approximation results for sums of Bernoulli, geometric, and logarithmic series random variables.

Słowa kluczowe

EN

convolution of distributions; poisson approximation; negative binomial approximation; power series distribution; Stein's method

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2022
• Tom: Vol. 42, Fasc. 1
• Strony: 63--80
• Opis fizyczny: Bibliogr. 19 poz., tab.

Twórcy

autor

Kumar A. N.

• Department of Mathematics Indian Institute of Technology, Bombay Powai, Mumbai 400076, India

autor

Vellaisamy P.

• Department of Mathematics Indian Institute of Technology, Bombay Powai, Mumbai 400076, India

autor

Viens F.

• Department of Statistics and Probability, Michigan State, University East Lansing, MI 48824, USA

Bibliografia

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