For an independent project I am trying to derive the cumulative function of the discrete phase type distribution. I was able to obtain the mass function: $f(x) = \alpha T^{(x-1)}t$ where $\alpha$ is the initial distribution, $T$ is the transient matrix (of dimension $(n-1) \times (n-1)$ and $t$ is the last column vector of the entire transition matrix P.
How do I obtain the cumulative distribution function from this?
