**5. Simulation**

In this section we present a Monte Carlo (MC) simulation study in order to illustrate the behavior of the ML estimators. We consider three sample sizes: *n* = 50, 150 and 300; two values for *σ*:1 and 2; two values for *λ*:3 and 4; and three values for *α*: 0.8, 1 and 2. For each combination of *n*, *σ*, *λ* and *α*, we draw 10,000 samples of size *n* from the GTPN(*<sup>σ</sup>*, *λ*, *α*) model. To simulate a value from this distribution, we consider the following scheme:


For each sample generated, ML estimators were computed numerically using the Newton-Raphson algorithm. Table 1 presents means and standard deviations for each parameter in each case. Notice that bias and standard deviations are reduced as the sample size increases, suggesting that the ML estimators are consistent.


**Table 1.** Monte Carlo (MC) simulation study for the maximum likelihood (ML) estimators in the GTPN(*σ*, *λ*, *α*) model in 12 combinations of *σ*, *λ* and *α*. The results
