**5. Simulation**

We present a simulation study to assess the performance of the EM algorithm for the parameters *σ* and *q* in the MSHN model. We consider 1000 samples of three sample sizes generated from the MSHN model: *n* = 30, 50 and 100. To generate *T* ∼ *MSHN*(*σ*; *q*) the following algorithm was used:


For each sample generated, the ML estimates were computed using the EM algorithm. Table 2 shows the mean of the bias estimated for each parameter (bias), its SE and the estimated root of the mean squared error (RMSE). From Table 2, we conclude that the ML estimates are quite stable. The bias is reasonable and diminishes as the sample size is increased. As expected, the terms SE and RMSE are closer when the sample size is increased, suggesting that the SE of the estimators is well estimated.

**Table 2.** Maximum likelihood (ML) estimations for parameters *σ* and *q* of the MSHN distribution. Standard error (SE), root of the mean squared error (RMSE).

