Closed form solution of correlation in doubly truncated or censored sample of bivariate log-normal distribution
Vilmunen, Jouko; Palmroos, Peter (21.08.2013)
Numero
17/2013Julkaisija
Bank of Finland
2013
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:bof-20140807180Tiivistelmä
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. Keywords: Bivariate log-normal distribution, Pearson's product-moment correlation, Truncated, Censored, Tail correlation, Solvency II JEL Classification C18, C46, G28