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Title: Approximations related to sum of $m$-dependent random variables Authors:  Neelesh Shankar Upadhye - Indian Institute of Technology Madras (India) [presenting]
Amit Kumar - Indian Institute of Technology Bombay (India)
Palaniappan Vellaisamy - Indian Institute of Technology Bombay (India)
Abstract: The sum of $m$-dependent random variables concentrated on $\mathbb{Z}_+=\{0,1,2,\dotsc\}$ is considered. We propose to approximate it with power series distributions and obtain the error bounds using Stein's method. We also discuss some relevant results for power series distributions such as Stein operator, uniform and non-uniform bounds for Stein magic factor, and etc. As special cases, we discuss two applications, namely, $2$-runs and $(k_1,k_2)$-runs and compare the bound with the existing bounds.