On discrete Gibbs measure approximation to runs

A. N. Kumar and N. S. Upadhye

Communications in Statistics - Theory and Methods, 2022, vol. 51, issue 5, 1488-1513

Abstract: A Stein operator for the runs is derived as a perturbation of an operator for discrete Gibbs measure. Due to this fact, using perturbation technique, the approximation results for runs arising from identical and non-identical Bernoulli trials are derived via Stein’s method. The bounds obtained are new and their importance is demonstrated through an interesting application.

Date: 2022
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DOI: 10.1080/03610926.2020.1765256

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