On Inequalities Involving Moments of Discrete Uniform Distributions
Some inequalities for the moments of discrete uniform distributions are obtained. The inequalities for the ratio and difference of moments are given. The special cases give the inequalities for the standard power means.
G.H. Hardy, J.E. Littlewood and G. Polya, Inequalities, New York, Cambridge University Press, Cambridge, U.K. (1934).
R. Sharma, R,G, Shandil, S. Devi and M. Dutta, Some Inequalities between Moments of probability distribution, J. Inequal. Pure and Appl. Math., 5 (2): Art. 86, (2004).
B.C. Rennie, On a Class of Inequalities, J. Austral. Math. Soc., 3: 442–448, (1963).
S. Ram, S. Devi, and R. Sharma, Some inequalities for the ratio and difference of moments, International Journal of Theoretical and Applied Sciences, 1(1): 103–110, (2009). http://dx.doi.org/10.1017/S1446788700039057
R. Sharma, A. Kaura, M. Gupta and S. Ram, Some bounds on sample parameters with refinements of Samuelson and Brunk inequalities. Journal of Mathematical Inequalities, 3:99–106, (2009). http://dx.doi.org/10.7153/jmi-03-09
R. Sharma, Some more inequalities for arithmetic mean, harmonic mean and variance, Journal of Mathematical Inequalities, 2: 109–114, (2008). http://dx.doi.org/10.7153/jmi-02-11
E.N. Laguerre, Surune mathode pour obtenir par approximation les raciness d’ une Equation algebrique qul a tautes ses raciness [in French], Nouvelles Annales de Mathematiques (Paris), 2e Serie 19: 161–171 and 193–202, (1980) [JFM12:71].
A. Lupas, Problem 246, Mathematicki vesnik (Belgrade), 8 (23): 333, (1971).
S.T. Jensen and G.P.H. Styan, Some comments and a bibliography on the Laguerre Samuelson inequalities with extensions and applications to statistics and matrix theory, Analytic and Geometric inequalities and their applications (Hari M. Srivastava and Themistocles M. Rassias, eds), Springer-Verlag, (1999).