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From |
Lulu Zeng <[email protected]> |

To |
"[email protected]" <[email protected]> |

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

Date |
Tue, 28 Jan 2014 21:04:47 +1100 |

Dear Alfonso and Roger, Thank you so much for your help. You are right that I incorrectly calculated the normal mean and sd from the log form. It is now fixed using the formula you suggested. Thank you again and have a great rest of the day! Best Regards, Lulu On Tue, Jan 28, 2014 at 12:00 AM, Roger B. Newson <[email protected]> wrote: > 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 > 1B Manresa Road > London SW3 6LR > UNITED KINGDOM > Tel: +44 (0)20 7352 8121 ext 3381 > Fax: +44 (0)20 7351 8322 > Email: [email protected] > Web page: http://www.imperial.ac.uk/nhli/r.newson/ > Departmental Web page: > http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/ > > 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 <[email protected]> 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 >>> * >>> * For searches and help try: >>> * http://www.stata.com/help.cgi?search >>> * http://www.stata.com/support/faqs/resources/statalist-faq/ >>> * http://www.ats.ucla.edu/stat/stata/ >> >> >> >> * >> * For searches and help try: >> * http://www.stata.com/help.cgi?search >> * http://www.stata.com/support/faqs/resources/statalist-faq/ >> * http://www.ats.ucla.edu/stat/stata/ >> > * > * For searches and help try: > * http://www.stata.com/help.cgi?search > * http://www.stata.com/support/faqs/resources/statalist-faq/ > * http://www.ats.ucla.edu/stat/stata/ * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

**Follow-Ups**:

**References**:**st: Random draw from log normal distribution with known mean and sd***From:*Lulu Zeng <[email protected]>

**Re: st: Random draw from log normal distribution with known mean and sd***From:*Alfonso Sánchez-Peñalver <[email protected]>

**Re: st: Random draw from log normal distribution with known mean and sd***From:*"Roger B. Newson" <[email protected]>

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