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I often assume that my data follow the normal distribution (concentrations of various pollutants in biota). The definition says that the data follow the log-normal distribution when normally distributed after logging. I see that when I plot my log data.

However, when I wanted to verify my choice of the distribution with the fitdistrplus package in R, I noticed some things I did not understand. The question is why when I chose "lnorm" distribution (fitdist(x, "lnorm"), the data poorly lie on a QQ-line, but when I chose norm for log x, the data fit the line very well (fitdist(log(x), "norm"). I thought that fitdist(x, "lnorm") should give the same results as fitdist(log(x), "norm").

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1 Answer 1

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In my simulation it gives the same estimates for the fitdist(log(x), "norm") and fitdist(x, "lnorm") and the histograms look ok. probably a typo in your code. or check how it handles missing data, maybe there is smth there

#code
#simulate lognormal sample
xxx = exp(rnorm(100, 0,1)) 
fitdist(xxx, "lnorm")
fitdist(log(xxx), "norm")

hist(log(xxx), probability = TRUE)
grid = seq(min(log(xxx)), max(log(xxx)), length.out = 100)
lines (x = grid, y =  dnorm(grid, mean(log(xxx)), sd(log(xxx)) ), 
        col = 2)

hist(xxx, probability = TRUE)
grid = seq(min(xxx), max(xxx), length.out = 100)
lines (x = grid, y =  dlnorm(grid, mean(xxx), sd(xxx) ), col = 2)

#results
## xxx = exp(rnorm(100, 0,1))
##> fitdist(xxx, "lnorm")
## Fitting of the distribution ' lnorm ' by maximum likelihood 
## Parameters:
##       estimate Std. Error
## meanlog  0.04965     0.1028
## sdlog    1.02820     0.0727
##> fitdist(log(xxx), "norm")
## Fitting of the distribution ' norm ' by maximum likelihood 
## Parameters:
##     estimate Std. Error
## mean  0.04965     0.1028
## sd    1.02820     0.0727

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  • $\begingroup$ Thank you for the reply. I run it again on my data - indeed, the parameters are the same, but still the figures look different. I thought that QQ-plot should look completely the same. Am I wrong? I uploaded both figures to 1drv.ms/u/s!AuRBSy2nUdUViahJEmwaUQi9p81Inw?e=brVewN $\endgroup$
    – ljb
    Dec 8, 2021 at 11:24
  • $\begingroup$ They look similar to me in the fit, the QQ have quantiles in the X-axis, so the same quantiles will spread differently in log- and non-logged space, so they can not be identical $\endgroup$
    – DianaS
    Dec 8, 2021 at 13:48
  • $\begingroup$ Thank You! Now I understand the issue. $\endgroup$
    – ljb
    Jan 6, 2022 at 10:11

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