Some improved tail bounds for the sum of variables with geometric distribution |
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Authors: | Dawei Lu Qing Liu Xinmei Shen |
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Institution: | 1. School of Mathematical Sciences, Dalian University of Technology, Dalian, Chinaludawei_dlut@163.com;3. School of Mathematical Sciences, Dalian University of Technology, Dalian, China |
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Abstract: | AbstractIn this paper, compared with the results in Janson (2018 Janson, S. 2018. Tail bounds for sums of geometric and exponential variables. Statistics & Probability Letters 135 (C):1–6. doi:10.1016/j.spl.2017.11.017.Crossref] , Google Scholar]), we provide some improved explicit bounds for the tail probabilities of the sum of independent geometric variables with their expectations and variances. Particularly, in some cases, we demonstrate that our bounds are sharper than the ones in Janson (2018 Janson, S. 2018. Tail bounds for sums of geometric and exponential variables. Statistics & Probability Letters 135 (C):1–6. doi:10.1016/j.spl.2017.11.017.Crossref] , Google Scholar]). |
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Keywords: | Geometric distribution tail probability probability generating function inequalities |
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