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From |
Alfonso Sánchez-Peñalver <[email protected]> |

To |
Stata List <[email protected]> |

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

Date |
Mon, 27 Jan 2014 07:51:43 -0500 |

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/

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

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