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Normal log-normal mixture, leptokurtosis and skewness

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  • Minxian Yang

Abstract

The normal log-normal mixture (NLNM) is considered for modelling leptokurtosis and skewness. The moment of the mixture is shown to be finite for any positive order. The expectations of exponential functions of the NLNM variable are also investigated. The kurtosis and skewness of the NLNM are explicitly shown to be determined by the variance of the log normal and the correlation between the normal and log normal. A set of cross-sectional data is fitted to the NLNM to illustrate that idiosyncratic variances may be modelled by the mixture.

Suggested Citation

  • Minxian Yang, 2008. "Normal log-normal mixture, leptokurtosis and skewness," Applied Economics Letters, Taylor & Francis Journals, vol. 15(9), pages 737-742.
    • Handle: RePEc:taf:apeclt:v:15:y:2008:i:9:p:737-742
    DOI: 10.1080/13504850600749073
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    Cited by:

    1. Adam, Klaus & Woodford, Michael, 2021. "Robustly optimal monetary policy in a new Keynesian model with housing," Journal of Economic Theory, Elsevier, vol. 198(C).
    2. Adam, Klaus & Woodford, Michael, 2018. "Leaning against housing prices as robustly optimal monetary policy," CFS Working Paper Series 601, Center for Financial Studies (CFS).
    3. Adam, Klaus & Woodford, Michael, 2018. "Leaning against housing prices as robustly optimal monetary policy," CFS Working Paper Series 601, Center for Financial Studies (CFS).
    4. Kashyap, Ravi, 2020. "David vs Goliath (You against the Markets), A dynamic programming approach to separate the impact and timing of trading costs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    5. Ravi Kashyap, 2016. "The Perfect Marriage and Much More: Combining Dimension Reduction, Distance Measures and Covariance," Papers 1603.09060, arXiv.org, revised Jul 2019.
    6. Kashyap, Ravi, 2021. "Artificial Intelligence: A Child’s Play," Technological Forecasting and Social Change, Elsevier, vol. 166(C).
    7. Stephane Hess & John Rose, 2012. "Can scale and coefficient heterogeneity be separated in random coefficients models?," Transportation, Springer, vol. 39(6), pages 1225-1239, November.
    8. Kashyap, Ravi, 2019. "The perfect marriage and much more: Combining dimension reduction, distance measures and covariance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    9. Michael Grabchak & Eliana Christou, 2021. "A note on calculating expected shortfall for discrete time stochastic volatility models," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 7(1), pages 1-16, December.
    10. Artiach, Miguel, 2012. "Leverage, skewness and amplitude asymmetric cycles," MPRA Paper 41267, University Library of Munich, Germany.
    11. Nicolae Tarbă & Mihai-Lucian Voncilă & Costin-Anton Boiangiu, 2022. "On Generalizing Sarle’s Bimodality Coefficient as a Path towards a Newly Composite Bimodality Coefficient," Mathematics, MDPI, vol. 10(7), pages 1-17, March.

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