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Moments and Cumulants of a Mixture

Author

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  • Christopher S. Withers

    (Industrial Research Limited)

  • Saralees Nadarajah

    (University of Manchester)

  • Shou Hsing Shih

    (American University of Sharjah)

Abstract

For the first time, general formulas for moments and cumulants are derived for mixtures of two or more distributions. The formulas involve the Bell polynomials. Computational efficiency of the formulas is illustrated by applications for two-component and three-component normal mixture models.

Suggested Citation

  • Christopher S. Withers & Saralees Nadarajah & Shou Hsing Shih, 2015. "Moments and Cumulants of a Mixture," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 541-564, September.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:3:d:10.1007_s11009-013-9379-y
    DOI: 10.1007/s11009-013-9379-y
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    References listed on IDEAS

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    1. Perez-Quiros, Gabriel & Timmermann, Allan, 2001. "Business cycle asymmetries in stock returns: Evidence from higher order moments and conditional densities," Journal of Econometrics, Elsevier, vol. 103(1-2), pages 259-306, July.
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    3. Di Nardo, E. & Guarino, G. & Senato, D., 2008. "Symbolic computation of moments of sampling distributions," Computational Statistics & Data Analysis, Elsevier, vol. 52(11), pages 4909-4922, July.
    4. P. A. Jacobs & P. A. W. Lewis, 1983. "Stationary Discrete Autoregressive‐Moving Average Time Series Generated By Mixtures," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(1), pages 19-36, January.
    5. D. Taylor, 1965. "Latency models for reaction time distributions," Psychometrika, Springer;The Psychometric Society, vol. 30(2), pages 157-163, June.
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    Cited by:

    1. Scaccia, Luisa & Marcucci, Edoardo & Gatta, Valerio, 2023. "Prediction and confidence intervals of willingness-to-pay for mixed logit models," Transportation Research Part B: Methodological, Elsevier, vol. 167(C), pages 54-78.

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