You can automatically choose the distribution for a particular gamlss model. First fit the model (say m1) with one distribution. Then use

chooseDist(m1, type="realline")

for distributions on the real line, i.e. (-inf,+inf),

or

chooseDist(m1, type="real plus")

for distributions on the positive real line, i.e. (0,+inf).

[If I have response variable y on the positive real line, then I find the best distribution for y on (0,+Inf).

Then I find the best distribution for log(y) on (-inf,+inf), and then create the corresponding log distribution, e.g. for TF by

gen.Family("TF", type="log")

and fit it.

The GAIC values of the best distributions can then be compared.

Note as others have said, the conditional distribution is being fitted (and not the marginal distribution).]

You can automatically choose the distribution for a particular gamlss model. First fit the model (say m1) with one distribution. Then use

chooseDist(m1, type="realline")

for distributions on the real line, i.e. (-inf,+inf),

or

chooseDist(m1, type="real plus")

for distributions on the positive real line, i.e. (0,+inf).

[If I have response variable y on the positive real line, then I find the best distribution for y on (0,+Inf).

Then I find the best distribution for log(y) on (-inf,+inf), and then create the corresponding log distribution, e.g. for TF by

gen.Family("TF", type="log")

and fit it.

The GAIC values of the best distributions can then be compared.

Note as others have said, the conditional distribution is being fitted (and not the marginal distribution).]