Consider the Generalized Student's T distribution, $T(\mu,\sigma^2,\nu)$.
Suppose $X_1 \sim T(\mu_1,\sigma_1^2,\nu_1)$ and $X_2 \sim T(\mu_2,\sigma_2^2,\nu_2)$, with $X_1$ and $X_2$ independent. What is $P(X_1 > X_2) = P(X_1 - X_2 > 0)$? Clearly, $E[X_1+X_2] = \mu_1+\mu_2$, but the rest isn't so clear.
Is there easily computable solution similar to: Probability of a point taken from a certain normal distribution will be greater than a point taken from another?
