Table 4 Numerical algorithm for our parameter estimation approach of our cost function (42)

Inputs:

– Strictly increasing sequence \(\{ t_{j} \} _{j = 1}^{M}\) of time points with \(t_{1} = 0\) and \(t_{M} = T\)

– Sequences \(\{ \widetilde{\widetilde{\alpha _{j}}} \} _{j = 2}^{M}\) and \(\{ \widetilde{\widetilde{\beta _{j}}} \} _{j = 2}^{M}\)

Step 1:

– Compute β̂ by (43)

Step 2:

– Compute \(\widehat{\gamma _{2}}\) by (45)

Step 3:

– Compute \(\widehat{\gamma _{1}}\) by (44)

Step 4:

– Compute \(\widehat{\alpha _{1}}\) and \(\widehat{\alpha _{2}}\) according to transformation (41)

Outputs:

– Parameters \(\widehat{\alpha _{1}}\), \(\widehat{\alpha _{2}}\), and β̂ for our parametric rates (39) and (40)