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Articles

An improved negative binomial approximation with high accuracy to the negative hypergeometric probability for order-preserving encryption

Pages 88-99 | Received 11 Apr 2016, Accepted 14 May 2016, Published online: 13 Jun 2016

References

  • A. Boldyreva, N. Chenette, Y. Lee, and A. O’neill, Order-preserving symmetric encryption, Advances in Cryptology-EUROCRYPT 2009, Springer Berlin Heidelberg, Cologne, 2009, pp. 224–241.
  • D.W. Brzezinski, Accuracy problems of numerical calculation of fractional order derivatives and integrals applying the Riemann--Liouville/Caputo formulas, Appl. Math. Nonlinear Sci. 1(1) (2016), pp. 23–43.
  • G.E. Crooks and S.E. Brenner, An alternative method of amino acid replacement, Bioinformacs 21 (2005), pp. 975–980.
  • J. Cuzick, Event-based analysis times for randomized clinical trials, Biometrika 88 (2001), pp. 245–253.
  • A. D’Elia and D. Piccolo, A mixture model for preferences data analysis, Comput. Stat. Data Anal. 49(3) (2005), pp. 917–934.
  • W.C. Guenther, The inverse hypergeometric -- a useful model, Stat. Neerl. 29(4) (1975), pp. 129–144.
  • F. Jian and S. Dandan, Complex network theory and its application research on P2P networks, Appl. Math. Nonlinear Sci. 1(1) (2016), pp. 44–50.
  • N.L. Johnson, A.W. Kemp, and S. Kotz, Univariate Discrete Distribution, John Wiley & Sons, New York, 2005.
  • K. Knopp, Theory and Application of Infinite Series, Blaekie, London, 1990.
  • F. López-Blázquez and B. Salamanca-Mino, Exact and approximated relations between negative hypergeometric and negative binomial probabilities, Commun. Stat. Theor. Methods 30(5) (2001), pp. 957–967.
  • D. Piccolo, Some approximations for the asymptotic variance of the maximum likelihood estimator of the parameter in the Inverse Hypergeometric random variable, Quaderni Stat. 3 (2001), pp. 215–229.
  • N.G. Sgourakis, P.G. Bagos, P.K. Papasaikas, and S.J. Hamodrakas, A method for the prediction of GPCRs coupling specificity to G-proteins using refined profile hidden Markov models, BMC Bioinf. 6(1) (2005), p. 1.
  • S. Singh and S.A. Sedory, A new randomized response device for sensitive characteristics: An application of the negative hypergeometic distribution, Metron 71(1) (2013), pp. 3–8.
  • K. Teerapabolarn, On the Poisson approximation to the negative hypergeometric distribution, Bull. Malays. Math. Sci. Soc. 34(2) (2011), pp. 331–336.
  • S. Wilks, Mathematical Statistics, John Wiley & Sons, New York, 1963.
  • L. Zhang, W. Xie, and W.D. Johnson, Performance of interval estimators for the inverse hypergeometric distribution, Commun. Stat. Simul. Comput. 44(5) (2015), pp. 1300–1310.

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