Understanding prediction output of zero-adjusted gamma model

#1
I am currently trying to implement a mixture model using the gamlss package in R. What I am trying to achieve is train a zero-adjusted gamma model on a training data set and then predicting values out of a test data set.
Setting up the model is no real problem, I do this by

ZAGA_Model = gamlss(formula = y~., sigma.formula = y~., nu.formula = y~., data = train_data, family = ZAGA)

Now when trying to get predictions for a new data set I am using the predictALL function

predictAll(ZAGA_Model, newdata = test_data, type = "response")

I get this output
$mu
[1] 400.9585 598.3456 297.5756 1988.7999 2057.1348 674.1622

$sigma
[1] 0.21363860 0.05586103 0.06269033 0.01436584 0.46865264 0.07960204

$nu
[1] 9.54167e-12 9.54167e-12 9.54167e-12 9.54167e-12 9.54167e-12 9.54167e-12

$y
[1] 403 710 349 1965 1300 550

The list of $y shows the actual values of the response variable in the test data set.
Now, what are my final predicted values? Is it just the "mu"? Is it the sum of "mu", "sigma" and "nu"? Or is it something completely different?

I didn't find anything online, so if anyone has something to read about it, it would be very much appreciated.
Thank you :)