Algorithm 1: Variational learning of the SD-HMM model.

1.    Initialize the shape and scale parameters of the SD distribution. 2.    Define the initial responsibilities. 3.    Compute $w^B,w^C$, and $w^{\pi }$. 4.    Initialize $B,C$, and $\pi$. 5.    while |old likelihood - new likelihood| ≥ 0 6.      Compute the data likelihood. 7.      Compute the responsibilities with the forward–backward procedure. 8.      Update the hyperparameters of the shape and scale parameters. 9.      Update $w^B,w^C$, and $w^{\pi }$ using responsibilities ${\gamma }^B,{\gamma }^C$, and ${\gamma }^{\pi }$. 10.    Update $B,C$, and $\pi$ using $w^B,w^C$, and $w^{\pi }$.