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From the gamlss.dist page for exGAUSS:

The ex-Gaussian distribution is often used by psychologists to model response time (RT). It is defined by adding two random variables, one from a normal distribution and the other from an exponential. The parameters mu and sigma are the mean and standard deviation from the normal distribution variable while the parameter nu is the mean of the exponential variable.

Here is how we're supposed to estimate the parameters:

library(gamlss)
y <- rexGAUS(100, mu = 300, nu = 100, sigma = 35)
m1 <- gamlss(y ~ 1, family = exGAUS)
m1

Unfortunately the estimates are way off:

Family:  c("exGAUS", "ex-Gaussian") 
Fitting method: RS() 

Call:  gamlss(formula = y ~ 1, family = exGAUS) 

Mu Coefficients:
(Intercept)  
      302.9  
Sigma Coefficients:
(Intercept)  
      3.496  
Nu Coefficients:
(Intercept)  
       4.63

A package that has disappeared from CRAN, retimes, can still be installed from 

https://cran.r-project.org/src/contrib/Archive/retimes/retimes_0.1-2.tar.gz
It has a function mexgauss: 
library(retimes)
mexgauss(y)

gives:

       mu     sigma       tau 
319.42880  55.51562  85.94403

which is closer.

mk9y
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    Are you asking a question here? Stack Overflow is a question and and answer site. It's not a place to post information. Perhaps you can edit your post to make it clear what your question is. – MrFlick Oct 11 '21 at 16:26
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    Note that a log link is used for sigma and nu by default, which I think could make the output a little confusing for those two parameters since output appears to be on the model (log) scale. – aosmith Oct 11 '21 at 16:36
  • @aosmith: your insight is obviously the solution that I should have seen. We know that nu = 100, log(100) = 4.605, which is close enough to the estimate of 4.63. Likewise log(sigma) = log(35) = 3.555, which close to the estimate of 3.496. The output of gamlss is indeed confusing, and could be made more explict. – mk9y Oct 11 '21 at 19:10
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    @MrFlick: I assumed that a grammatically-defined question in the subject of an SE question would be sufficient. Please let me know if a grammatically-defined question is also required in the body of an SE question. – mk9y Oct 01 '22 at 13:01

1 Answers1

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The estimates for sigma and nu do appear to be way off in the model output. This is because exGaus() uses a log link for both those parameters by default. From the documentation, showing the defaults:

exGAUS(mu.link = "identity", sigma.link = "log", nu.link = "log")

The output shows results on the model scale so the estimates for those two parameters are given on the log scale.

If we exponentiate the results for sigma and nu then we get estimates that look more reasonable and much closer to what we'd expect.

# estimated sigma should be close to 35
exp(3.496)
#> [1] 32.98325

# estimated nu shoud be close to 100
exp(4.63)
#> [1] 102.5141

Created on 2021-10-11 by the reprex package (v2.0.0)

aosmith
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