APPLICATIONS OF MATHEMATICAL INEQUALITIES IN STATISTICS

The fundamental inequalities such as Tchebyshev's integral inequality for synchronous (asynchronous) mappings, Holder's integral inequality, Cauchy-Buniakowski-Schwartz integral inequality have been consistently applied in estimating some special functions and characterizing probability distribution functions. New estimations based on these inequalities have been derived for gamma and beta functions and the moments and moment ratios of gamma and beta distributions. Main aim of this research is to estimate the general moments of the probability distributions and to characterize distribution functions.

[10] Pranesh Kumar, “The Ostrowski Type Moment Integral Inequalities and Moment-Bounds for Continuous Random Variables”.Computers and Mathematics with Applications, 49,11-12, pp. 1929-40, 2005. ( pdf )

[9] Pranesh Kumar, "Inequalities Involving Moments of a Continuous Random Variable Defined Over a Finite Interval" Computers and Mathematics with Applications, 48, pp. 257-73,2004. (pdf)

[8] Pranesh Kumar, “Moments Inequalities of a Random Variable Defined over a Finite Interval”. Inequality Theory and Applications-Volume 2, Y. J. Cho, J. K. Kim, S. S. Dragomir; Eds., Nova Science Publishers, NY,147-164, 2003.

[7] Pranesh Kumar, "Moment Inequalities Of A Random Variable Defined Over A Finite Interval", Jour. Inequalities in Pure and Applied Math.,3(3),article 41, 2002. ( pdf )

[6] Pranesh Kumar, "Hermite-Hadamard Inequalities And Their Applications In Estimating Moments", Inequality Theory and Applications (In Press). ( pdf )

[5] Pranesh Kumar, S.P.Singh and S.S.Dragomir, "Some Inequalities Involving Beta And Gamma Functions", Nonlinear Analysis Forum, 6(1),pp. 143-150,2001. ( pdf )

[4] S.S.Dragomir, Pranesh Kumar and S.P.Singh, "Mathematical Inequalities With Applications To The Beta And Gamma Mappings-II”, Indian Journal of Mathematics,2000. ( pdf )

[3] S.S.Dragomir, Pranesh Kumar and S.P.Singh, "Mathematical Inequalities With Applications To The Beta And Gamma Mappings-I”, Indian Journal of Mathematics,2000. ( pdf )

[2] Pranesh Kumar and S.S Dragomir, "Some Inequalities For The Gamma Functions And Moment Ratios Of Gamma Variables", Indian Journal of Mathematics,1999.

[1] S.S. Dragomir, N.M. Dragomir and K. Pranesh, “An Inequality For Logarithms And Applications In Information Theory”, Computers and Mathematics with Applications,38,2, 11-17,1999. ( pdf )