Log logistic

[yunzli]

Hi:

I think it might be good to include LogLogistic distribution in the package.

[devmotion]

Thank you for the PR! Before I add more detailed comments, I wonder if we should use an alternative parameterization that is consistent with the logistic distribution. Is there a specific reason for why you chose the parameterization in this PR? An advantage of the other parameterization would be that LogLogistic would be consistent with Logistic. In all other cases (LogNormal, LogitNormal, and LogUniform) the parameters are consistent with the "original" distributions, i.e., Normal and Uniform. I assume that consistent parameters will also make it easier to use the existing implementation of Logistic.

[yunzli]

Hi, using the alternative parameterization is an option. However, to my knowledge, alternative parameterization has not been used widely in research papers. With the current parameterization, the parameter θ serves as a scale parameter and median of the distribution. The alternative parameterization doesn't have such interpretations.

[ParadaCarleton]

Hi, using the alternative parameterization is an option. However, to my knowledge, alternative parameterization has not been used widely in research papers. With the current parameterization, the parameter θ serves as a scale parameter and median of the distribution. The alternative parameterization doesn't have such interpretations.

We could use a keyword constructor for the parametrization currently being used (in terms of θ).

[devmotion]

I think for consistency we should use the same parameters as for Logistic here - also in the case of e.g. LogNormal we don't use the (possibly) more interpretable median but the mean of the normal distribution it is constructed from.

[ParadaCarleton]

I think for consistency we should use the same parameters as for Logistic here - also in the case of e.g. LogNormal we don't use the (possibly) more interpretable median but the mean of the normal distribution it is constructed from.

Yep, sorry, I was agreeing; just offering a suggestion about how to add an extra parametrization. (I'd definitely enjoy seeing parametrizations for both the LogNormal and the LogLogistic in terms of their geometric mean/median using keyword constructors.)

[yunzli]

I think for consistency we should use the same parameters as for Logistic here - also in the case of e.g. LogNormal we don't use the (possibly) more interpretable median but the mean of the normal distribution it is constructed from.

It is possible to make re-parameterization internally so we can use the existing implementation of Logistic? My concern is that it is common to use the same parameterization for LogNormal and Normal, but not for LogLogistic and Logistic.

[ParadaCarleton]

I think for consistency we should use the same parameters as for Logistic here - also in the case of e.g. LogNormal we don't use the (possibly) more interpretable median but the mean of the normal distribution it is constructed from.

It is possible to make re-parameterization internally so we can use the existing implementation of Logistic? My concern is that it is common to use the same parameterization for LogNormal and Normal, but not for LogLogistic and Logistic.

I think I've seen this parametrization for the log-logistic before in papers (mostly in economics), so I don't think it's all that uncommon. I assume the popularity of each varies by field.

[yunzli]

I think for consistency we should use the same parameters as for Logistic here - also in the case of e.g. LogNormal we don't use the (possibly) more interpretable median but the mean of the normal distribution it is constructed from.

It is possible to make re-parameterization internally so we can use the existing implementation of Logistic? My concern is that it is common to use the same parameterization for LogNormal and Normal, but not for LogLogistic and Logistic.

I think I've seen this parametrization for the log-logistic before in papers (mostly in economics), so I don't think it's all that uncommon. I assume the popularity of each varies by field.

Hi, thank you for providing that information. Can you give me some references? I couldn't find any. Thank you again.