We consider the problem of estimating tail probabilities of random sums of scale mixture of phase-type distributions -a class of distributions corresponding to random variables which can be represented as a product of a non-negative but otherwise arbitrary random variable with a classical phasetype random variable. Our motivation arises from applications in risk, queueing problems for estimating ruin probabilities, and waiting time distributions respectively. Classical rare-event simulation

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... rithms cannot be implemented in this setting because these methods typically rely on the availability of the cumulative distribution function or the moment generating function, but these are difficult to compute or not even available for the class of scale mixture of phase-type distributions. In this paper, we address these issues and propose alternative simulation methods for estimating tail probabilities of random sums of scale mixture of phase-type distributions; our algorithm combines importance sampling and conditional Monte Carlo methods. The empirical performance of the method suggested is explored via numerical experimentation.