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Coverage probability of prediction intervals for discrete random variables

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  • Wang, Hsiuying

Abstract

Prediction interval is a widely used tool in industrial applications to predict the distribution of future observations. The exact minimum coverage probability and the average coverage probability of the conventional prediction interval for a discrete random variable have not been accurately derived in the literature. In this paper, procedures to compute the exact minimum confidence levels and the average confidence levels of the prediction intervals for a discrete random variable are proposed. These procedures are illustrated with examples and real data applications. Based on these procedures, modified prediction intervals with the minimum coverage probability or the average coverage probability close to the nominal level can be constructed.

Suggested Citation

  • Wang, Hsiuying, 2008. "Coverage probability of prediction intervals for discrete random variables," Computational Statistics & Data Analysis, Elsevier, vol. 53(1), pages 17-26, September.
    • Handle: RePEc:eee:csdana:v:53:y:2008:i:1:p:17-26
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    References listed on IDEAS

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    1. J. F. Lawless & Marc Fredette, 2005. "Frequentist prediction intervals and predictive distributions," Biometrika, Biometrika Trust, vol. 92(3), pages 529-542, September.
    2. Peter Hall & Andrew Rieck, 2001. "Improving coverage accuracy of nonparametric prediction intervals," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(4), pages 717-725.
    3. Basu, Ruma & Ghosh, J. K. & Mukerjee, Rahul, 2003. "Empirical Bayes prediction intervals in a normal regression model: higher order asymptotics," Statistics & Probability Letters, Elsevier, vol. 63(2), pages 197-203, June.
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    Cited by:

    1. Annika Homburg & Christian H. Weiß & Layth C. Alwan & Gabriel Frahm & Rainer Göb, 2021. "A performance analysis of prediction intervals for count time series," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(4), pages 603-625, July.
    2. Wang, Hsiuying, 2009. "Comparison of p control charts for low defective rate," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4210-4220, October.
    3. N. Balakrishnan & E. Beutner & E. Cramer, 2013. "Computational aspects of statistical intervals based on two Type-II censored samples," Computational Statistics, Springer, vol. 28(3), pages 893-917, June.
    4. K. Krishnamoorthy & Shanshan Lv, 2018. "Highest posterior mass prediction intervals for binomial and poisson distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(7), pages 775-796, October.
    5. Qinglong Tian & Daniel J. Nordman & William Q. Meeker, 2022. "Constructing Prediction Intervals Using the Likelihood Ratio Statistic," INFORMS Joural on Data Science, INFORMS, vol. 1(1), pages 63-80, April.

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