I am looking for a Hoeffding-type result that bounds the tail of a sum of independent, but not identically distributed random variables. Let X_1,..,X_n be independent exponential random variables with rates k_1,...,k_n. (Note: X_i's are unbounded unlike the case considered by Hoeffding)(adsbygoogle = window.adsbygoogle || []).push({});

Let S= \sum_{i=1}^{n} X_i. I am interested in bounding P(S>a). I am looking for tighter bounds than Markov's Inequality and Chebyshev's Inequality. Is anyone here aware of well-known results in this direction?

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# Sums of Independent (but not identically distributed) Random Variables

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