I have a probability density function $f(x)$ that is based on two parameters $p$,$q$. Using mixing rule, I created another density function $$g(x) = C\cdot F(x) + (1-C)\cdot G(x) $$ where $F(x)$ is $f(x)$ using $p_1,q_1$ as parameters and $G(x)$ is $f(x)$ using $p_2,q_2$ as parameters. How do I determine if it is possible for $g(x)$ to be bimodal? To make it clear, I do not know the values of $p_1,q_1,p_2,q_2,C$. At this point, I just want to know if bimodality is possible for atleast one set of $(p_1,q_1,p_2,q_2,C)$.
I tried using bimodality coefficient as described in https://en.wikipedia.org/wiki/Multimodal_distribution However, the coefficient I get is very large (order of $10^{38}$) and I am not sure if the approach is correct. Any help is much appreciated.
