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Jul 28th, 2015
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  1. m = .1; s = .4
  2. sg = sqrt(log(1 + s^2/m^2)); sg
  3. ## 1.683215
  4. mu = log(m) - .5*sg^2; mu
  5. ## -3.719192
  6. x = rnorm(10^6, mu, sg); y = exp(x)
  7. mean(x); sd(x)
  8. ## -3.720081
  9. ## 1.682534
  10. mean(y); sd(y)
  11. ## 0.09942132
  12. ## 0.4097221
  13.  
  14. m = .1; s = .2
  15. mu = log(m^2/sqrt(s^2 + m^2)); mu
  16. ## -3.107304
  17. sg = sqrt(log(1+s^2/m^2)); sg
  18. ## 1.268636
  19. x = rnorm(10^6, mu, sg)
  20. mean(x); sd(x)
  21. ## -3.107111
  22. ## 1.269737
  23. y = exp(x)
  24. mean(y); sd(y)
  25. ## 0.1000590
  26. ## 0.1992975
  27.  
  28. y = rlnorm(10^6, -11.4511, 3.0144); mean(y); sd(y) # Your values
  29. ## 0.0009537684
  30. ## 0.03262853 # not right
  31. y = rlnorm(10^6, -3.107304, 1.268636); mean(y); sd(y) # m=.1, s=.2
  32. ## 0.1003433
  33. ## 0.2027905
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