Context: I have a set of data that is bimodal, so I used the mixtools package in R to fit a bimodal normal distribution to it. It looked as if the normal did not fit very well, and given other similar sets of data that I have (that are not bimodal) and are log-normally distributed, I figured log-normal would probably make more sense. However, mixtools does not have a way to fit a bimodal log-normal distribution, so I took the log of the data and refit. This image is below, and it fits to my satisfaction.
Really, this is kind of a software issue (not knowing what package could explicitly fit a bimodal log-normal) but it's made me think about something I have wondered often: is fitting a normal distribution to logged data equivalent to fitting a log-normal distribution to the original data? I suspect not, but I am not sure why? (Ignoring cases of having zeros or negative data. Assuming all data are fairly large positives, but skewed). Also knowing that of course you'd need to back transform to get to the original value estimates.
I tried to test this out with some toy data and realized I don't even know why the meanlog associated with a log-normal distribution is NOT what you get when you take the mean of the logged normal distribution. So maybe my understanding is already broken when it comes to the log-normal's parameters.
library(fitdistrplus) set.seed(1) test <- rnorm(1000, mean=100) test[test<=0] <- NA #Unnecessary since no values <= 0, but just to prove test<-na.omit(test) log.test <- log10(test) mean(log.test) sd(log.test) #1.999926 is mean for log.test #0.004496153 is sd for log.test fitdist(log.test, dist="lnorm", method="mle") #However, "meanlog" is 0.693107737 and "sdlog" is 0.002247176 #The means are so different, not sure why?