Approximate Confidence Interval for the Mean of Poisson Distribution

Author(s)
Manad Khamkong

Affiliation(s)

Department of Statistics, Faculty of Science, Chiang Mai University, Chiang Mai, Thailand.

Department of Statistics, Faculty of Science, Chiang Mai University, Chiang Mai, Thailand.

ABSTRACT

A Poisson distribution is well used as a standard model for analyzing count data. Most of the usual constructing confidence intervals are based on an asymptotic approximation to the distribution of the sample mean by using the Wald interval. That is, the Wald interval has poor performance in terms of coverage probabilities and average widths interval for small means and small to moderate sample sizes. In this paper, an approximate confidence interval for a Poisson mean is proposed and is based on an empirically determined the tail probabilities. Simulation results show that the pro- posed interval outperforms the others when small means and small to moderate sample sizes.

A Poisson distribution is well used as a standard model for analyzing count data. Most of the usual constructing confidence intervals are based on an asymptotic approximation to the distribution of the sample mean by using the Wald interval. That is, the Wald interval has poor performance in terms of coverage probabilities and average widths interval for small means and small to moderate sample sizes. In this paper, an approximate confidence interval for a Poisson mean is proposed and is based on an empirically determined the tail probabilities. Simulation results show that the pro- posed interval outperforms the others when small means and small to moderate sample sizes.

KEYWORDS

Confidence Interval; Coverage Probability; Poisson Distribution; Expected Width; Wald Interval

Confidence Interval; Coverage Probability; Poisson Distribution; Expected Width; Wald Interval

Cite this paper

M. Khamkong, "Approximate Confidence Interval for the Mean of Poisson Distribution,"*Open Journal of Statistics*, Vol. 2 No. 2, 2012, pp. 204-207. doi: 10.4236/ojs.2012.22024.

M. Khamkong, "Approximate Confidence Interval for the Mean of Poisson Distribution,"

References

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[4] K. Krishnamoorthy and J. Peng, “Improved Closed-Form Prediction Intervals for Binomial and Poisson Distribution,” Journal of Statistical Planning and Inference, Vol. 141, No. 5, 2011, pp. 1709-1718. doi:10.1016/j.jspi.2010.11.021

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[8] R Development Core Team, “R: A Language and Environment for Statistical Computing,” R Foundation for Statistical Computing, Vienna, 2011.

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[1] T. T. Cai, “One-Sided Confidence Intervals in Discrete Distributions,” Journal of Statistical Planning and Inference, Vol. 131, No. 1, 2005, pp. 63-88. doi:10.1016/j.jspi.2004.01.005

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

[3] Y. Guan, “Moved Score Confidence Intervals for Means of Discrete Distributions,” American Open Journal Statistics, Vol. 1, 2001, pp. 81-86. doi:10.4236/ojs.2011.12009

[4] K. Krishnamoorthy and J. Peng, “Improved Closed-Form Prediction Intervals for Binomial and Poisson Distribution,” Journal of Statistical Planning and Inference, Vol. 141, No. 5, 2011, pp. 1709-1718. doi:10.1016/j.jspi.2010.11.021

[5] J. Stamey and C. Hamillton, “A Note on Confidence Intervals for a Linear Function of Poisson Rates,” Communications in Statistics-Theory and Methods, Vol. 35, No. 4, 2005, pp. 849-856. doi:10.1080/03610920802255856

[6] M. B. Swifi, “Comparison of Confidence Intervals for a Poisson Mean-Further Considerations,” Communications in Statistics-Theory and Methods, Vol. 38, No. 5, 2009, pp. 748-759.

[7] L. A. Barker, “Comparison of Nine Confidence Intervals for a Poisson Parameter When the Expected Number of Events Is ≤ 5,” The American Statistician, Vol. 56, No. 2, 2002, pp. 85-89. doi:10.1198/000313002317572736

[8] R Development Core Team, “R: A Language and Environment for Statistical Computing,” R Foundation for Statistical Computing, Vienna, 2011.

[9] N. Gurtler and N. Henze, “Recent and Classical Goodness-of-Fit Tests for the Poisson Distribution,” Journal of Statistical Planning and Inference, Vol. 90, No. 2, 2000, pp. 207-225. doi:10.1016/S0378-3758(00)00114-2

[10] P. Blaesild and J. Granfeldt, “Statistics with Applications in Biology and Geology,” Chapman & Hall/CRC, New York, 2003.