dtpt gives the density, ptpt gives the distribution function and rtpt generates random deviates.
The length of the result is determined by n for rtpt, and is the maximum of the lengths of the numerical arguments for the other functions.
The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.
A variable have tpt distribution with parameters \(\sigma>0\), \(\lambda \in\) R and \(\nu>0\) if its probability density
function can be written as
$$
f(y; \sigma, \lambda, q) = \frac{t_\nu\left(\frac{y}{\sigma}-\lambda\right)}{\sigma T_\nu(\lambda)}, y>0,
$$
where \(t_\nu(\cdot)\) and \(T_\nu(\cdot)\) denote the density and cumultative distribution functions for the standard t distribution with \(\nu\) degrees of freedom.