Re: st: Random draw from log normal distribution with known mean and sd

["Roger B. Newson" <r.newson@imperial.ac.uk>]

Another useful source on the lognormal distributon (I find) is Stas 
Kolenikov's page at

http://www.komkon.org/~tacik/science/lognorm.pdf

which presents the useful formulas in one place.

Best wishes

Roger

Roger B Newson BSc MSc DPhil
Lecturer in Medical Statistics
Respiratory Epidemiology, Occupational Medicine
and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton Campus
Room 33, Emmanuel Kaye Building
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Opinions expressed are those of the author, not of the institution.

On 27/01/2014 12:51, Alfonso Sánchez-Peñalver wrote:
> Hi Lulu,
>
> please explain how you get the equivalent normal mean and sd of -1.04 and 0.89 from the lognormal mean and sd of -0.22 and 0.74? Because I think that is where the problem is. Check http://en.wikipedia.org/wiki/Log-normal_distribution to see the relationship with the means and the standard deviations. The following seems close enough
>
> clear
> set obs 5000
> generate n = rnormal(-2.77, 1.58)
> generate ln = -exp(n)
> summarize
>
> Best,
>
> Alfonso
>
> On Jan 27, 2014, at 4:15 AM, Lulu Zeng <luluzengnz@gmail.com> wrote:
>
> > Dear Statalist,
> >
> > I am seeking your help on take random draws from a log normal
> > distribution (with known mean and sd). I am aware similar question has
> > been answered on below page but I didn't manage to solve my issue with
> > this (http://www.stata.com/statalist/archive/2005-04/msg00999.html).
> >
> > I am trying to calculate Willingness to Pay (wtp) for a number of
> > attributes (variables) of a random utility model (mixed logit in my
> > case).
> >
> > wtp for a particular attribute is defined as the ratio of the
> > coefficient for the attribute (e.g., engine performance) to the
> > coefficient for the price variable. However, both of the engine
> > performance and price coefficients are random in my model -
> > performance is normally distributed & price is lognormal distributed.
> >
> > Given the difference in distribution for the two coefficients, I had
> > to use simulation to work out the wtp. That means - take random draws
> > from both distribution and divide one by another to work out a
> > distribution for wtp.
> >
> > To achieve this, my first step was to take random draws from my log
> > normally distributed price coefficient, which has a log mean & log sd
> > of -0.22 and 0.74 respectively (equivalent to a normal mean & sd of
> > -1.04 and 0.89 respectively). These figures are the results from my
> > model (distribution of the coefficient).
> >
> > I used below code to take the draw as suggested by the webpage above
> > (1200 draws):
> >
> > gen lognormal = exp(-1.04 + 0.89 * invnorm(uniform()))
> >
> > To check, I summed the resulting draws from the above, and the draws a
> > mean of 0.53 & sd of 0.56. These figures are the same as the -0.22 and
> > 0.74 I have above in log form, so I thought there must be something
> > wrong.
> >
> > It would be really appreciated if I could have your help on this.
> >
> >
> > Best Regards,
> > Lulu
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