Hi all,
If I have two attributes of time: lognormally distributed and correlated as following:
time1 < exp(m1 + s1 * draws1)
time2 < exp(m2 + s2 * draws2 + s1_2 * draws1)
Now if I want to find the mean and sd for the random variable time2,
is this the correct way of doing that?
Find the unconditionals from the model and find mean and sd as following:
mean = mean(as.vector(unconditionals$time2))
sd = sd(as.vector(unconditionals$time2))
Is this the correct way of finding mean and sd? (Or for narrower distribution using conditionals instead of unconditional)
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Mean and SD of lognormal attribute correlated with another attribute

 Site Admin
 Posts: 558
 Joined: 24 Apr 2020, 16:29
Re: Mean and SD of lognormal attribute correlated with another attribute
Hi
yes, you can use the unconditionals function in that way, or you can also use the analytical formula for the mean and variance of a lognormal  with enough draws, they will converge to each other.
You should never use the conditionals for this purpose
Stephane
yes, you can use the unconditionals function in that way, or you can also use the analytical formula for the mean and variance of a lognormal  with enough draws, they will converge to each other.
You should never use the conditionals for this purpose
Stephane
Re: Mean and SD of lognormal attribute correlated with another attribute
Thank you for the prompt reply,
One more thing
Does the correlation term s1_2 comes somewhere in the analytical formula?
I know generally we use mean= exp(m + s^2/2), but its the correlation parameter s1_2 that’s confusing me.
One more thing
Does the correlation term s1_2 comes somewhere in the analytical formula?
I know generally we use mean= exp(m + s^2/2), but its the correlation parameter s1_2 that’s confusing me.

 Site Admin
 Posts: 558
 Joined: 24 Apr 2020, 16:29
Re: Mean and SD of lognormal attribute correlated with another attribute
Yes, you would need to replace s by sqrt(s2^2+s1_2^2)
Re: Mean and SD of lognormal attribute correlated with another attribute
Thank you for clearing that out..