Refinements of Gaussian Tail Inequality

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N. A. Rather
T. A. Rather


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.

Probability inequalities, Gaussian tail inequality, probability density function

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How to Cite
A. Rather, N., & A. Rather, T. (2018). Refinements of Gaussian Tail Inequality. Asian Journal of Probability and Statistics, 1(3), 1-8.
Original Research Article