I need to cite the pdf(density) or cdf(distribution function) of a non-central scaled Student's t distribution.
There is an article about the non-central Student's t distribution http://en.wikipedia.org/wiki/Noncentral_t-distribution. But I have found no article that states the pdf or cdf and which also considers a scaling parameter. Note that the distribution should be scaled independently of the shape parameter $\nu$.
In particular a parametrization as in the
gamlss.dist package, function
TF2, would be nice - i.e. mean $\mu$, degrees of freedom $\nu$ and a scale $\sigma$ that corresponds to the standard deviation.
Has anyone seen something alike in a paper or book?
Many thanks!!! Jo