Markov–Krein theorem

In probability theory, the Markov–Krein theorem gives the best upper and lower bounds on the expected values of certain functions of a random variable where only the first moments of the random variable are known.^[1][2][3][4] The result is named after Andrey Markov and Mark Krein.^[5]

The theorem can be used to bound average response times in the M/G/k queueing system.^[6]

References

1. Stokes, S. Lynne; Mulry-Liggan, Mary H. (1987). "Estimation of Interviewer Variance for Categorical Variables" (PDF). Journal of Official Statistics. 3: 389–401. Retrieved 11 June 2013.
2. Brockett, P. L.; Kahane, Y. (1992). "Risk, Return, Skewness and Preference". Management Science. 38 (6): 851. doi:10.1287/mnsc.38.6.851.
3. Simar, L. (1976). "Maximum Likelihood Estimation of a Compound Poisson Process". The Annals of Statistics. 4 (6): 1200. doi:10.1214/aos/1176343651. JSTOR 2958588.
4. Karlin, S.; Studden, W. J. (1966). Tchebycheff Systems, with Applications in Analysis and Statistics. New York: Interscience. p. 82.
5. Kreĭn, M. G. (1959). "The ideas of P. L. Čebyšev and A. A. Markov in the theory of limiting values of integrals and their further development". Amer. Math. Soc. Transl. 2 (12): 1–121. MR 0113106.
6. Gupta, V.; Osogami, T. (2011). "On Markov–Krein characterization of the mean waiting time in M/G/K and other queueing systems". Queueing Systems. 68 (3–4): 339. doi:10.1007/s11134-011-9248-8.