Error Bounds for Trapezoid Type Quadrature Rules with Applications for the Mean and Variance

  • Pietro Cerone
  • Sever S. Dragomir
  • Eder KikiantyEmail author
Part of the Springer Optimization and Its Applications book series (SOIA, volume 91)


In this paper, we establish some inequalities of trapezoid type to give tight bounds for the expectation and variance of a probability density function. The approach is also demonstrated for higher order moments.


Probability Density Function Error Bound Bounded Variation Type Inequality Gaussian Random Variable 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Pietro Cerone
    • 1
  • Sever S. Dragomir
    • 2
    • 3
  • Eder Kikianty
    • 4
    Email author
  1. 1.Department of Mathematics and StatisticsLa Trobe UniversityBundooraAustralia
  2. 2.School of Engineering and ScienceVictoria UniversityMelbourneAustralia
  3. 3.School of Computational and Applied MathematicsUniversity of the WitwatersrandWitwatersrandSouth Africa
  4. 4.Department of MathematicsUniversity of JohannesburgAuckland ParkSouth Africa

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