An Approximation for the Inverse Distribution Function of a Combination of Random Variables, with an Application to Operating Theatres

A new approximation introduced elsewhere is employed to approximate the inverse distribution function of a combination of random variables with known and finite first four moments. Its accuracy is thence demonstrated for four arbitrary combinations, the unknown distribution of which is artificially constructed through Monte-Carlo simulation. The new approximation performs better than the regularly applied normal approximation. An application to the problem of determining the control period needed to assess utilization rate of operating theatres is presented along with Monte-Carlo simulation results. Implications for queueing systems are indicated.