This function computes the probability density of the Asymmetric Triangular distribution given parameters (\(\nu\), \(\omega\), and \(\psi\)) computed by partri. The probability density function is
$$f(x) = \frac{2(x-\nu)}{(\omega - \nu)(\psi - \nu)}\mbox{,}$$
for \(x < \omega\),
$$f(x) = \frac{2(\psi-x)}{(\psi - \omega)(\psi - \nu)}\mbox{,}$$
for \(x > \omega\), and
$$f(x) = \frac{2}{(\psi - \nu)}\mbox{,}$$
for \(x = \omega\)
where \(x(F)\) is the quantile for nonexceedance probability \(F\), \(\nu\) is the minimum, \(\psi\) is the maximum, and \(\omega\) is the mode of the distribution.