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The family of positive tempered α-stable (pTAS) or sometimes also tempered one-sided α-stable distributions dates back to Tweedie (1984) and Hougaard (1986) who discussed it in the context of frailty distribution in life table methods for heterogenous populations. The pTAS family generalizes the well-known gamma distribution and allows for heavier tails depending on the parameter α. Because of this...
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