*6.2. Application 2*

The second dataset is taken from Von Alven [16], and represents 46 instances of active repairs (in hours) for an airborne communication transceiver. Some descriptive statistics are: mean = 3.607, variance = 24.445, skewness = 2.888, and kurtosis = 11.802.

Initially we computed the moment estimators for the MSHN distribution, obtaining the following estimations: *σM* = 2.407 and *qM* = 2.635. We used these estimations as initial values in computing the ML estimators presented in Table 5. For each distribution we report the estimated log-likelihood.


**Table 5.** ML estimations with the corresponding SE for the models fitted.

Table 6 displays the AIC and BIC for each model fitted. Figure 5 presents the histogram of the data fitted with the HN, SHN and MSHN distributions, provided with the ML estimations.



**Figure 5.** Histogram fitted with the HN, SHN and MSHN distributions provided with the ML estimations.
