*6.3. Application 3*

The third data set (Linhart and Zucchini [17]) represents 31 times of air conditioning system failure of an aeroplane. Some descriptive statistics are: mean = 55.35, variance = 5132.503, skewness = 1.805, and kurtosis = 5.293.

Initially we computed the moment estimators for the MSHN distribution, and obtained the following estimations: *σM* = 38.125 and *qM* = 2.743. We used these estimations as initial values in computing the ML estimators presented in Table 7. For each distribution we report the estimated log-likelihood.


**Table 7.** ML estimations with the corresponding SE for the models fitted.

Table 8 displays the AIC and BIC for each model fitted. Figure 6 presents the histogram of the data fitted with the HN, SHN and MSHN distributions, provided with the ML estimations.


 313.715

 316.583 **311.908**

**314.776**

AIC

BIC

 325.7224

 327.1564

**Figure 6.** Histogram fitted with the HN, SHN and MSHN distributions provided with the ML estimations.
