Abstract:The geometric sum plays a significant role in risk theory and reliability theory [Kalashnikov (1997)] and a prototypical example of the geometric sum is Rényi's theorem [Rényi (1956)] saying a sequence of suitably parameterised geometric sums converges to the exponential distribution. There is extensive study of the accuracy of exponential distribution approximation to the geometric sum [Sugakova (1995), Kalashnikov (1997), Peköz & Röllin (2011)] but there is little study on its natural counterpart of gamma di… Show more
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