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Appendix 



A random variable X is considered to be lognormally distributed when the natural logarithm of X, Y=ln(X), has a 

 normal distribution. Specifically, if Y is normally distributed with mean u^ and standard deviation ct ln , then X=e Y 

 is lognormally distributed with density function (Aitchison & Brown 1969): 



1 

 The kth moment about zero, E(X k ) is expressed as 



exp 



f-(lnZ-u LN ) 2 



2o 2 , 



(AD 



£(X k ) = E (e kY ) = exp ^u^ + 



2 J 



<A2) 



In particular, 



Population Mean = u = exp 



Hln + 



(A3) 



Variance (X) - a 2 = [exp (0%) - 1] • [exp (2u LN + a 2 m )], 



(A4) 



Geometric Mean = Median (X) = exp (Uln)- 



(A5) 



