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Mean and SD of lognormal attribute correlated with another attribute

Ask questions about post-estimation functions (e.g. prediction, conditionals, etc) or other processing of results.
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Niranjan
Posts: 12
Joined: 01 Feb 2021, 23:27

Mean and SD of lognormal attribute correlated with another attribute

Post by Niranjan » 17 Jan 2022, 10:07

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)

stephanehess
Site Admin
Posts: 558
Joined: 24 Apr 2020, 16:29

Re: Mean and SD of lognormal attribute correlated with another attribute

Post by stephanehess » 17 Jan 2022, 10:58

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
--------------------------------
Stephane Hess
www.stephanehess.me.uk

Niranjan
Posts: 12
Joined: 01 Feb 2021, 23:27

Re: Mean and SD of lognormal attribute correlated with another attribute

Post by Niranjan » 17 Jan 2022, 12:15

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.

stephanehess
Site Admin
Posts: 558
Joined: 24 Apr 2020, 16:29

Re: Mean and SD of lognormal attribute correlated with another attribute

Post by stephanehess » 18 Jan 2022, 08:08

Yes, you would need to replace s by sqrt(s2^2+s1_2^2)
--------------------------------
Stephane Hess
www.stephanehess.me.uk

Niranjan
Posts: 12
Joined: 01 Feb 2021, 23:27

Re: Mean and SD of lognormal attribute correlated with another attribute

Post by Niranjan » 18 Jan 2022, 09:09

Thank you for clearing that out..

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