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The American Statistician Volume 49, 1995 - Issue 2
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The Moment Bound is Tighter than Chernoff's Bound for Positive Tail Probabilities

Thomas K. Philips IBM Retirement Fund, Stamford, CT, 06904, USA; Advanced Research, Rogers, Casey and Associates, Darien, CT, 06820, USA
&
Randolph Nelson IBM Research Division, Thomas J. Watson Research Center, York-town Heights, NY, 10598, USA; Investment Research, OTA Limited Partnership, Purchase, NY, 10577, USA
Pages 175-178 | Received 01 Jun 1993, Published online: 27 Feb 2012

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StevenG. From. (2012) A Comparison of the Moment and Factorial Moment Bounds for Discrete Random Variables. The American Statistician 66:4, pages 214-216.
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Gianluca Fusai, Daniele Marazzina, Marina Marena & Michael Ng. (2012) Z-Transform and preconditioning techniques for option pricing. Quantitative Finance 12:9, pages 1381-1394.
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H. Gzyl, P. L. Novi Inverardi & A. Tagliani. (2008) A Proposal for a New Bound for Discrete Distributions. Communications in Statistics - Theory and Methods 37:14, pages 2149-2161.
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M. N. Goria & A. Tagliani. (2003) Bounds on the Tail Probability and Absolute Difference Between Two Distributions. Communications in Statistics - Theory and Methods 32:3, pages 519-532.
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BruceG. Lindsay & Prasanta Basak$suffix/text()$suffix/text(). (2000) Moments Determine the Tail of a Distribution (But Not Much Else). The American Statistician 54:4, pages 248-251.
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Philippe Naveau. (1997) Comparison between the Chernoff and Factorial Moment Bounds for Discrete Random Variables. The American Statistician 51:1, pages 40-41.
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Articles from other publishers (4)

Tobias Johnson & Erol Peköz. (2022) Concentration inequalities from monotone couplings for graphs, walks, trees and branching processes. Stochastic Processes and their Applications 152, pages 1-31.
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Gianluca Fusai, Daniele Marazzina & Marina Marena. (2011) Pricing Discretely Monitored Asian Options by Maturity Randomization. SIAM Journal on Financial Mathematics 2:1, pages 383-403.
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Chengzhi Li & Wei Zhao. (2009) Stochastic performance analysis of non-feedforward networks. Telecommunication Systems 43:3-4, pages 237-252.
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Sheldon M. Ross. (2009) Using the Importance Sampling Identity to Bound Tail Probabilities. Probability in the Engineering and Informational Sciences 12:4, pages 445-452.
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