Refinements of Gaussian Tail Inequality
N. A. Rather
Department of Mathematics, University of Kashmir, Srinagar, 190006, India
T. A. Rather *
Department of Mathematics, University of Kashmir, Srinagar, 190006, India
*Author to whom correspondence should be addressed.
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