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Variance of the truncated negative binomial distribution

Author

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  • Shonkwiler, J.S.

Abstract

Citations to formulas for the moments of the truncated negative binomial distribution usually reference the paper by Gurmu and Trivedi (1992). However their second moments of the truncated negative binomial are incorrect. We derive the correct second moments for both the left and right truncated negative binomial distribution. The second moments of the truncated distributions are written in a form that shows they will converge to the second moment of the un-truncated distribution when the truncated first moment approaches the un-truncated first moment.

Suggested Citation

  • Shonkwiler, J.S., 2016. "Variance of the truncated negative binomial distribution," Journal of Econometrics, Elsevier, vol. 195(2), pages 209-210.
    • Handle: RePEc:eee:econom:v:195:y:2016:i:2:p:209-210
    DOI: 10.1016/j.jeconom.2016.09.002
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    References listed on IDEAS

    as
    1. Cameron,A. Colin & Trivedi,Pravin K., 2013. "Regression Analysis of Count Data," Cambridge Books, Cambridge University Press, number 9781107667273, January.
    2. Gurmu, Shiferaw & Trivedi, Pravin K., 1992. "Overdispersion tests for truncated Poisson regression models," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 347-370.
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    Cited by:

    1. Kajal Dihidar & Manjima Bhattacharya, 2017. "Estimating Sensitive Population Proportion Using A Combination Of Binomial And Hypergeometric Randomized Responses By Direct And Inverse Mechanism," Statistics in Transition New Series, Polish Statistical Association, vol. 18(2), pages 193-210, June.
    2. Dihidar Kajal & Bhattacharya Manjima, 2017. "Estimating Sensitive Population Proportion Using a Combination of Binomial and Hypergeometric Randomized Responses by Direct and Inverse Mechanism," Statistics in Transition New Series, Statistics Poland, vol. 18(2), pages 193-210, June.
    3. Leonardo Egidi & Ioannis Ntzoufras, 2020. "A Bayesian quest for finding a unified model for predicting volleyball games," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(5), pages 1307-1336, November.

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    More about this item

    Keywords

    Negative binomial; Truncation; Incomplete beta function;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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