Moved Score Confidence Intervals for Means of Discrete Distributions

Author(s)
Yu Guan

ABSTRACT

Let*X* denote a discrete distribution as Poisson, binomial or negative binomial variable. The score confidence interval for the mean of X is obtained based on inverting the hypothesis test and the central limit theorem is discussed and recommended widely. But it has sharp downward spikes for small means. This paper proposes to move the score interval left a little (about 0.04 unit), called by moved score confidence interval. Numerical computation and Edgeworth expansion show that the moved score interval is analogous to the score interval completely and behaves better for moderate means; for small means the moved interval raises the infimum of the coverage probability and improves the sharp spikes significantly. Especially, it has unified explicit formulations to compute easily.

Let

Cite this paper

nullY. Guan, "Moved Score Confidence Intervals for Means of Discrete Distributions,"*Open Journal of Statistics*, Vol. 1 No. 2, 2011, pp. 81-86. doi: 10.4236/ojs.2011.12009.

nullY. Guan, "Moved Score Confidence Intervals for Means of Discrete Distributions,"

References

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[8] L. D. Brown, T. T. Cai and A. DasGupta, “Interval Estimation in Exponential Families,” Statistica Sinica, Vol. 13, 2003, pp. 19-49.

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[10] X. H. Zhou, C. M. Li and Z. Yang, “Improving Interval Estimation of Binomial Proportions,” Philosophical Transactions of the Royal Society A, Vol. 366, No. 1874, 2008, pp. 2405-2418. doi:10.1098/rsta.2008.0037

[1] P. Kabaila and J. Byrne, “Exact Short Poisson Confidence Intervals,” Canadian Journal of Statistics, Vol. 29, No. 1, 2001, pp. 99-106. doi:10.2307/3316053

[2] A. Agresti and B. Coull, “Approximate Is Better than ‘Exact’ for Interval Estimation of Binomial Proportions,” The American Statistician, Vol. 52, No. 2, 1998, pp.119-126. doi:10.2307/2685469

[3] L. D. Brown, T. T. Cai and A. DasGupta, “Interval Estimation intervals for a Binomial Proportion and Asymptotic Expansion,” The Annals of Statistics, Vol. 30, No. 1, 2002, pp.160-201.

[4] G. Casella and R. L. Berger, “Statistical Inference,” 2nd Edition, Wadsworth, West Yorkshire, 2002.

[5] J. Byrne and P. Kabaila, “Comparison of Poisson Confidence Intervals,” Communications in Statistics-Theory and Methods, Vol. 34, No. 3, 2005, pp. 545-556. doi:10.1081/STA-200052109

[6] A. Agresti and B. Caffo, “Simple and Effective Confidence Intervals for Proportions and Differences of Proportions Result from Adding Two Successes and Two Failures,” The American Statistician, Vol. 54, No. 4, 2000, pp. 280-288. doi:10.2307/2685779

[7] L. D. Brown, T. T. Cai and A. DasGupta, “Confidence Intervals for a Binomial Proportion and Asymptotic Expansion,” The Annals of Statistics, Vol. 30, No. 1, 2002, pp. 160-201.

[8] L. D. Brown, T. T. Cai and A. DasGupta, “Interval Estimation in Exponential Families,” Statistica Sinica, Vol. 13, 2003, pp. 19-49.

[9] S. E. Vollset, “Confidence Intervals for a Binomial Proportion,” Statistics in Medicine, Vol. 12, No. 9, 1993, pp. 809-824. doi:10.1002/sim.4780120902

[10] X. H. Zhou, C. M. Li and Z. Yang, “Improving Interval Estimation of Binomial Proportions,” Philosophical Transactions of the Royal Society A, Vol. 366, No. 1874, 2008, pp. 2405-2418. doi:10.1098/rsta.2008.0037