本論文修正 Mahmoud 和 Alam (2010)的廣義線性指數分配及 Sarhan et al. (2013)的冪次方廣義線性指數分配提出一個新的分配—修正的冪次方廣義線性指數分配。此分配的重要性在於它可以靈活地分析不同類型的壽命資料，從加速壽命測試到地震、洪水、降雨量、超市及醫院的排隊等候資料。針對此一新的分配，我們推導出一些數學和統計上的特性，以及樣本最大及最小統計量的漸近分配。

A generalization of the generalized linear exponential distribution proposed by Mahmoud and Alam (2010) and its extension, exponentiated generalized liner exponential distribution proposed by Sarhan et al. (2013), is introduced and studied. The importance of this distribution lies in its flexibility for analyzing different types of lifetime data ranging from accelerated life testing through to earthquakes, floods, rainfall, queues in supermarkets and others. We discuss some mathematical and statistical properties. In addition, we give results on the asymptotic distributions for sample extreme order statistics.

1 Introduction 1
2 Some Mathematical Properties 4
3 Some Statistical Properties 8
3.1 Moments of Order Statistics 8
3.2 Mean Residual Lifetime 11
3.3 Asymptotic Distributions 14
4 Maximum Likelihood Estimation 16
5 Concluding Remarks 18
6 Appendix 19
7 References 25
Figure 1 Plots of the density functions of the MEGLED 5
Figure 2 Plots of the hazard rate functions of the MEGLED 6

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