Part of the Springer Optimization and Its Applications book series (SOIA, volume 91)
Error Bounds for Trapezoid Type Quadrature Rules with Applications for the Mean and Variance
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.
KeywordsProbability Density Function Error Bound Bounded Variation Type Inequality Gaussian Random Variable
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
- 3.Cacoullos, T. Variance inequalities, characterizations, and a simple proof of the central limit theorem. Data analysis and statistical inference, 27–32 (1992)Google Scholar
- 4.Cacoullos, T. and Papadatos, N. and Papathanasiou, V.: Variance inequalities for covariance kernels and applications to central limit theorems. Teor. Veroyatnost. i Primenen. 42, No. 1, 195–201 (1997)Google Scholar
- 5.Cerone P., and Dragomir S.S.: Trapezoid type rules from an inequalities point of view. Handbook of Analytic Computational Methods in Applied Mathematics. Anastassiou G. (Ed.), pp. 65–134. CRC Press, N.Y. (2000)Google Scholar
- 6.Chang, W-Y. and Richards, D.St.P.: Variance inequalities for functions of multivariate random variables. Contemp. Math. 234, 43–67 (1999)Google Scholar
© Springer International Publishing Switzerland 2014