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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

    ()
    (Bank of Finland Research)

  • Palmroos, Peter

    ()
    (Financial Supervisory Authority)

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    Abstract

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

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    File URL: http://www.suomenpankki.fi/en/julkaisut/tutkimukset/keskustelualoitteet/Documents/BoF_DP_1317.pdf
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    Bibliographic Info

    Paper provided by Bank of Finland in its series Research Discussion Papers with number 17/2013.

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    Length: 9 pages
    Date of creation: 21 Aug 2013
    Date of revision:
    Handle: RePEc:hhs:bofrdp:2013_017

    Contact details of provider:
    Postal: Bank of Finland, P.O. Box 160, FI-00101 Helsinki, Finland
    Web page: http://www.suomenpankki.fi/en/
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    Related research

    Keywords: bivariate log-normal distribution; Pearson's product-moment correlation; truncated; censored; tail correlation; solvency II;

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    1. 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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