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The PDF and CF of Pearson type IV distributions and the ML estimation of the parameters

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  • Nagahara, Yuichi

Abstract

Recently, in the area of finance, especially for the risk management, some heavy-tailed and skewed distributions are strongly required. The Pearson type IV distribution can represent various kurtosis and skewness. However, it has not been used for practical purpose because of the difficulties of its implementation. This paper discusses the practical methods which could overcome various difficulties involved. Type IV is defined explicitly by the "skewed version" of type VII. The general normalizing constant is newly obtained. The application for stock returns distribution are shown. The method of evaluating the tail probabilities is developed. The implementation of the Pearson type IV distribution could make a breakthrough for statistical modeling.

Suggested Citation

  • Nagahara, Yuichi, 1999. "The PDF and CF of Pearson type IV distributions and the ML estimation of the parameters," Statistics & Probability Letters, Elsevier, vol. 43(3), pages 251-264, July.
    • Handle: RePEc:eee:stapro:v:43:y:1999:i:3:p:251-264
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    Citations

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    Cited by:

    1. Alem MERDIĆ & Kadrija HODŽIĆ, 2022. "Global Competitiveness Index 4.0 and export performances of the European economies," Theoretical and Applied Economics, Asociatia Generala a Economistilor din Romania - AGER, vol. 0(3(632), A), pages 43-60, Autumn.
    2. Yuichi Nagahara, 2011. "Using Nonnormal Distributions to Analyze the Relationship Between Stock Returns in Japan and the US," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 18(4), pages 429-443, November.
    3. Choi, Pilsun & Nam, Kiseok, 2008. "Asymmetric and leptokurtic distribution for heteroscedastic asset returns: The SU-normal distribution," Journal of Empirical Finance, Elsevier, vol. 15(1), pages 41-63, January.
    4. Norberto Rodríguez, 2000. "Bayesian Model Estimation and Selection for the Weekly Colombian Exchange Rate," Borradores de Economia 161, Banco de la Republica de Colombia.
    5. Yuichi Nagahara, 2003. "Non‐Gaussian Filter and Smoother Based on the Pearson Distribution System," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(6), pages 721-738, November.
    6. Sree Vinutha Venkataraman & S. V. D. Nageswara Rao, 2016. "Estimation of dynamic VaR using JSU and PIV distributions," Risk Management, Palgrave Macmillan, vol. 18(2), pages 111-134, August.
    7. Nagahara, Yuichi, 2004. "A method of simulating multivariate nonnormal distributions by the Pearson distribution system and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 47(1), pages 1-29, August.
    8. Sima Ahmadpour & Tat-Chee Wan & Zohreh Toghrayee & Fariba HematiGazafi, 2017. "Statistical Analysis of Video Frame Size Distribution Originating from Scalable Video Codec (SVC)," Complexity, Hindawi, vol. 2017, pages 1-12, March.
    9. Stavroyiannis, S. & Makris, I. & Nikolaidis, V. & Zarangas, L., 2012. "Econometric modeling and value-at-risk using the Pearson type-IV distribution," International Review of Financial Analysis, Elsevier, vol. 22(C), pages 10-17.
    10. Patra, Saswat, 2021. "Revisiting value-at-risk and expected shortfall in oil markets under structural breaks: The role of fat-tailed distributions," Energy Economics, Elsevier, vol. 101(C).
    11. Fabio Pizzutilo, 2013. "The Distribution of the Returns of Japanese Stocks and Portfolios," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 3(9), pages 1249-1259, September.
    12. Zhu, Ke & Li, Wai Keung, 2013. "A new Pearson-type QMLE for conditionally heteroskedastic models," MPRA Paper 52344, University Library of Munich, Germany.
    13. Verhoeven, Peter & McAleer, Michael, 2004. "Fat tails and asymmetry in financial volatility models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 64(3), pages 351-361.
    14. C. García & J. García Pérez & J. Dorp, 2011. "Modeling heavy-tailed, skewed and peaked uncertainty phenomena with bounded support," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 20(4), pages 463-486, November.
    15. Muino, J.M. & Voit, E.O. & Sorribas, A., 2006. "GS-distributions: A new family of distributions for continuous unimodal variables," Computational Statistics & Data Analysis, Elsevier, vol. 50(10), pages 2769-2798, June.
    16. Stavros Stavroyiannis, 2016. "Value-at-Risk and backtesting with the APARCH model and the standardized Pearson type IV distribution," Papers 1602.05749, arXiv.org.
    17. Lai, Jing-yi, 2012. "Shock-dependent conditional skewness in international aggregate stock markets," The Quarterly Review of Economics and Finance, Elsevier, vol. 52(1), pages 72-83.

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