# The Confidence Interval of the Coefficient of Variation for a Zero - Inflated Poisson Distribution

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## Abstract

This research was to present the confidence interval of the coefficient of variation for Zero-Inflated Poisson (ZIP) distribution by using the principle parameter estimation of ZIP distribution with Maximum Likelihood Estimator and to create the confidence interval of the coefficient of variation for ZIP distribution. The efficiency of the interval was considered by the coverage probability and the average width of the confidence interval. The R program was employed to simulate the repetition of numerous data set, which coefficient of variation (κ) was at 0.39 to 3.32. The parameters of ZIP distribution were average number of events in a specified region (λ), equal to 5(5)25. The proportions of observed zero (ω) were 0.1(0.1)0.9 and the sample sizes (n) were 30, 40, 50, 100 and 200 with the confidence levels of 0.90, 0.95 and 0.99. The results showed that at the confidence levels of 0.90 and 0.95, the proposed confidence interval gave the coverage probability as criteria defined in all cases of λ when n = 50, 100, 200 and ω = 0.2–0.9. For the confidence level of 0.99, found that the coverage probability meets the defined criteria in all cases of ω when n = 200 and λ = 20, 25 In addition, the results showed that the average width of the proposed confidence interval decreases when ω increase. However, as n increases, the average width of the confidence interval decreases for all levels of λ and ω.

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## References

[2] J. Vandenbroek, “A score test for zero inflation in a Poisson-distribution,” International Biometric Society, vol. 51, no. 2, pp. 738–743, 1995.

[3] D. Bohning, E. Dietz, P. Schlattmann, L. Mendonca, and U. Kirchner, “The zero-inflated Poisson model and the decayed, missing and filled teeth index in dental epidemiology,” Journal of the Royal Statistical Society Series A-Statistics in Society, vol. 162, no. 2, pp. 195–209, 1999.

[4] M. Xie, B. He, and TN. Goh, “Zero-inflated Poisson model in statistical process control,” Computational Statistics & Data Analysis, vol. 38, pp. 191–201, 2001.

[5] V. Peerajit and T. Mayureesawan, “Nonconforming control charts for zero-inflated Processes,” M.S. thesis, Department of Applied Statistics, Faculty of Applied Statistics King Mongkut’s University of Technology North Bangkok, 2009 (in Thai).

[6] N. Katemee and T. Mayureesawan, “Control charts for zero-inflated Poisson models,” Applied Mathematical Sciences, vol. 6, no. 56, pp. 2791-2803, 2012.

[7] P. Yip, “Inference about the mean of a Poisson distribution in the presence of a nuisance parameter,” Australian Journal of Statistics, vol. 30, pp. 299–306, 1988.

[8] J. P. Boucher, M. Denuit, and M. Guillen, “Number of accidents or number of claims? An approach with zero-inflated Poisson models for panel data,” Journal of Risk and Insurance, vol. 76, no. 4, pp. 821–845, 2009.

[9] J. J. V. Veen, A. Gatt, A. E. Bowyer, P. C. Cooper, S. Kitchen, and M. Makris, “Calibrated automated thrombin generation and modified thromboelastometry in haemophilia A,” Journal of Thrombosis Research, vol. 123, pp. 895–901, 2009.

[10] E. G. Miller and M. J. Karson, “Testing the equality of two coefficients of variation,” in American Statistical Association: Proceedings of the Business and Economics Secti on, Part I, 1977, pp. 278–283.

[11] J. Gong and Y. Li, “Relationship between the estimated Weibull modulus and the coefficient of variation of the measured strength for ceramics,” Journal of the American Ceramic Society, vol. 82, pp. 449–452, 1999.

[12] K. Ko, K. Kim, and J. Huh, “Variations of wind speed in time on Jeju Island, Korea,” Journal of Energy, vol. 35, pp. 3381–3387, 2010.

[13] K. N. Krishnakumar, G. S. L. H. V. Prasadarao, and C. S. Gopakumar, “Rainfall trends in twentieth century over Kerala, India.” Journal of Atmospheric Environment, vol. 43, pp. 1940–1944, 2009.

[14] A. B. Lashak, M. Zare, H. Abedi, and M. Y. Radan, “The application of coefficient of variations in earthquake forecasting,” Journal of Seismology and Earthquake Engineering; Tehran, vol. 11, no. 2, pp. 55–62, 2009.

[15] H. A. Majd, J. Hoseini, H. Tamaddon, and A. A. Baghban, “Comparison of the precision of measurements in three types of micropipettes according to NCCLS EP5-A2 and ISO 8655-6,” Journal of Paramedical Sciences (JPS), vol. 1, no. 3, pp. 2–8, 2010.

[16] M. G. Vangel, “Confidence intervals for a normal coefficient of variation,” American Statistician, vol. 50, pp. 21–26, 1996.

[17] A. T. MaKay, “Distribution of the coefficient of variation and the extended “t” distribution,” Journal of the Royal Statistical Society, vol. 95, no. 4, pp. 695–698, 1932.

[18] B. Iglewicz and R.H. Myers, “Comparisons of approximations to the percentage points of the sample coefficient of variation,” Technometrics, vol. 12, pp. 166–169, 1970.

[19] W. Panichkitkosolkul, “Improved confidence intervals for a coefficient of variation of a normal distribution,” Thailand Statistician, vol. 7, no. 2, pp. 193–199, 2009 (in Thai).

[20] W. Panichkitkosolkul, “A simulation comparision of new confidence intervals for the coefficient of variation of Poisson distribution,” Silpakorn University Science and Technology Journal, vol. 4, no. 2, pp. 14–20, 2010 (in Thai).

[21] S. Numna and J. Naratip, “Analysis of extra zero counts using zero-inflated Poisson models,” M.S. thesis, Department of Mathematics and Statistics, Faculty of Science, Prince of Songkla University, 2009 (in Thai).

[22] N. L. Johnson, A. W. Kemp, and S. Kotz, Univariate Discrete Distributions, 3rd ed. New York: Wiley, 2005.