Refinements of Gaussian Tail Inequality
Asian Journal of Probability and Statistics · pp. 1–8 · Published 4 Sep 2018
10.9734/ajpas/2018/v1i324541Abstract
In this paper, we first prove a theorem which gives considerably better bound for 0 ≤ t ≤ 1/2 than Gaussian tail inequality (or tail bound for normal density) and thus is a refinement of Gaussian tail inequality in this case. Next we present an interesting result which provides a refinement of Gaussian tail inequality for t > √ 3. Besides, we also prove an improvement of Gaussian tail inequality for 0 < t ≤ 1/2. Finally, we present a more general result which includes a variety of interesting results as special cases.
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