Risk management and risk measures like value at risk and conditional value at risk originated in the financial and insurance industries. In recent years, the interest in risk management and risk measurement has spread over all industrial sectors. Finance and insurance applications focused on continuous data like financial return, profit or loss. In other contexts, e.g. in operational risk management, discrete count data are of like importance. The present study analyses theoretical and empirical aspects of the risk measures value at risk, tail conditional expectation, conditional value at risk under the binomial, negative binomial, and Poisson distribution. Particular emphasis is on interval estimation of the risk measures. Copyright © 2011 John Wiley & Sons, Ltd.