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Closed form solution of correlation in doubly truncated or censored sample of bivariate log-normal distribution

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  • Vilmunen, Jouko
  • Palmroos, Peter

Abstract

In this study we present a closed form solution to the moments and, in particular, correlation of two log-normally distributed random variables, where the underlying log-normal distribution is potentially truncated and censored at both tails. Throughout the analysis we further assume that the parameters of the unconstrained bivariate log-normal distribution are known. The closed form solution also covers the cases where one tail is truncated and the other is censored.

Suggested Citation

  • Vilmunen, Jouko & Palmroos, Peter, 2013. "Closed form solution of correlation in doubly truncated or censored sample of bivariate log-normal distribution," Bank of Finland Research Discussion Papers 17/2013, Bank of Finland.
    • Handle: RePEc:zbw:bofrdp:rdp2013_017
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    References listed on IDEAS

    as
    1. Bebu, Ionut & Mathew, Thomas, 2009. "Confidence intervals for limited moments and truncated moments in normal and lognormal models," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 375-380, February.
    2. Lien, Da-Hsiang Donald, 1985. "Moments of truncated bivariate log-normal distributions," Economics Letters, Elsevier, vol. 19(3), pages 243-247.
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    More about this item

    Keywords

    Bivariate log-normal distribution; Pearson's product-moment correlation; Truncated; Censored; Tail correlation; Solvency II;
    All these keywords.

    JEL classification:

    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation

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