**5. Simulation Results**

We assessed the performance of the MLE approach with respect to various samples size. The assessment was based on a simulation study:


$$\text{Bias}(\theta) = \frac{1}{1000} \sum\_{j=1}^{1000} \left(\hat{\theta}\_{j} - \theta\right) \text{ and } \text{MSE}(\theta) = \frac{1}{1000} \sum\_{j=1}^{1000} \left(\hat{\theta}\_{j} - \theta\right)^{2}.$$

ˆ

The empirical results for complete data are given in Tables 10–14 using OEHLIEx(1.5, 0.5,0.9), OEHLIEx(2.5,2.5,2.5), OEHLIEx(0.5,0.8,0.9), and OEHLIEx(0.5,0.5,0.5), respectively. Whereas the empirical results for type-II censored data when *k* = 20 are given in Tables 15–17 for OEHLIEx(0.7,0.8,0.9), OEHLIEx(0.5,1.5,2.5), OEHLIEx(0.01,0.5,0.1.5), and OEHLIEx(0.1,1.5,0.5), respectively.


**Table 10.** The bias and MSE (in parentheses) for schema I.

**Table 11.** The bias and MSE (in parentheses) for schema II.


**Table 12.** The bias and MSE (in parentheses) for schema III.


**Table 13.** The bias and MSE (in parentheses) for schema IV.



**Table 14.** The bias and MSE (in parentheses) for schema V.

**Table 15.** The bias and MSE (in parentheses) for VI.


**Table 16.** The bias and MSE (in parentheses) for VII.


**Table 17.** The bias and MSE (in parentheses) for VIII.


From Tables 10–17, we can say that the MLE approach can be used effectively to estimate the model parameters for both a small and large sample size. This due to the consistency properties of the estimators when *n* grows.
