Closed Form Solution of Correlation in Doubly Truncated or Censored Sample of Bivariate Log-Normal Distribution

13 Pages Posted: 28 Sep 2013

See all articles by Jouko Vilmunen

Jouko Vilmunen

Bank of Finland, Research Unit

Peter Palmroos

Bank of Finland - Finnish Financial Supervision Authority (FIN-FSA)

Date Written: August 21, 2013

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.

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

JEL Classification: C18, C46, G28

Suggested Citation

Vilmunen, Jouko and Palmroos, Peter, Closed Form Solution of Correlation in Doubly Truncated or Censored Sample of Bivariate Log-Normal Distribution (August 21, 2013). Bank of Finland Research Discussion Paper No. 17/2013, Available at SSRN: https://ssrn.com/abstract=2331214 or http://dx.doi.org/10.2139/ssrn.2331214

Jouko Vilmunen

Bank of Finland, Research Unit ( email )

P.O. Box 160
FIN-00101 Helsinki
Finland

Peter Palmroos (Contact Author)

Bank of Finland - Finnish Financial Supervision Authority (FIN-FSA) ( email )

Snellmaninkatu 6
P.O. Box 159
FIN-00101 Helsinki
Finland

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