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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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Stavros Stavroyiannis, 2016. "Value-at-Risk and backtesting with the APARCH model and the standardized Pearson type IV distribution," Papers 1602.05749, arXiv.org.
    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. 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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