Refinements of Gaussian Tail Inequality

Main Article Content

N. A. Rather
T. A. Rather

Abstract

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.

Keywords:
Probability inequalities, Gaussian tail inequality, probability density function

Article Details

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. https://doi.org/10.9734/ajpas/2018/v1i324541
Section
Original Research Article