Extended gamma processes have been seen as a flexible extension of standard gamma processes in the recent reliability literature, for the purpose of cumulative deterioration modeling. The probabilistic properties of the standard gamma process have been well explored since the 1970s, whereas those of its extension remain largely unexplored. In particular, stochastic comparisons between degradation levels modeled by standard gamma processes and ageing properties for the corresponding level-crossing times are now well understood. The aim of this paper is to explore similar properties for extended gamma processes and see which ones can be broadened to this new context. As a by-product, new stochastic comparisons for convolutions of gamma random variables are also obtained.

中文翻译：

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扩展伽马过程的随机比较和老化特性

在最近的可靠性文献中，扩展伽马过程已被视为标准伽马过程的灵活扩展，用于累积劣化建模。自 1970 年代以来，标准伽马过程的概率特性已得到很好的探索，而其扩展的概率特性在很大程度上仍未得到探索。特别是，通过标准伽马过程建模的退化水平与相应水平交叉时间的老化特性之间的随机比较现在已经很好地理解了。本文的目的是探索扩展伽马过程的类似特性，看看哪些特性可以扩展到这一新环境。作为副产品，还获得了伽马随机变量卷积的新随机比较。