  Real-time systems are a set of programs, a scheduling policy and a system
architecture, constrained by timing requirements. Most of daily embedded
devices are real-time systems, e.g. airplanes, cars, trains, spatial probes,
etc. The time required by a program for its end-to-end execution is called its
response time. Usually, upper-bounds of response times are computed in order to
provide safe deadline miss probabilities. In this paper, we propose a suited
re-parametrization of the inverse Gaussian mixture distribution adapted to
response times of real-time systems and the estimation of deadline miss
probabilities. The parameters and their associated deadline miss probabilities
are estimated with an adapted Expectation-Maximization algorithm.
