Stein factors for negative binomial approximation in Wasserstein distance. (English) Zbl 1329.62077

Barbour, A. D.; Gan, H. L.; Xia, A.

Bernoulli 21, No. 2, 1002-1013 (2015).

Essential ingredients of Stein’s method for probability approximation include bounds on the solution of the Stein equation (referred to as Stein factors, or magic factors). This paper gives such bounds for negative binomial approximation in the Wasserstein distance. The proof of the Stein factors is probabilistic, and builds upon techniques developed in [A. D. Barbour and A.-H. Xia, Bernoulli 12, No. 6, 943–954 (2006; Zbl 1328.62076)] to find analogous bounds in the Poisson case.
These Stein factors are applied to give an explicit bound in the negative binomial approximation of the number of parasites in a host under a model which allows for a varying rate of ingestion of parasites over time. The Wasserstein metric is useful here since the infectivity of a host can be expected to be proportional to the number of parasites it carries.

Reviewer: Fraser Daly (Edinburgh)

MSC:

62E17	Approximations to statistical distributions (nonasymptotic)
62E10	Characterization and structure theory of statistical distributions
62P10	Applications of statistics to biology and medical sciences; meta analysis

Keywords:

negative binomial approximation; Stein’s method; Stein factors; Wasserstein distance; parasite model

Citations:

Zbl 1328.62076

References:

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