Here is my question.
I want to get the unconditional PDF of a random variable t with PDF $f(t\mid\tau_1,\tau_2,\dots,\tau_n)$. Depending on the relation between $\tau_1,\tau_2,\dots,\tau_n$, I have two choices. One is that, when $\tau_1=\tau_2=\cdots=\tau_n$, I have $f_1(t\mid\tau_1,\tau_2,\dots,\tau_n)$. The other is that, when $\tau_i \neq \tau_j, i \neq j$, I have $f_2(t\mid\tau_1,\tau_2,\dots,\tau_n)$.
Which one should I choose to get the unconditional PDF of $t$, when I use $f(t) = \int\cdots\int f(t\mid\tau_1,\tau_2,\dots,\tau_n)\,d\tau_1d\,\tau_2\cdots d\tau_n$?
I have tried $f_2$, since it seems more general, but the analysis result does not match the simulation result well. So could some one offer me some suggestions?
Thanks so much!.