Some properties of the failure rate function for mixtures of Erlang distributions

Abstract

We study some properties of the failure rate for a mixture of Erlang distributions. In particular, we discuss mixtures of Erlang distributions with the same scale parameter and we describe the behavior of the failure rate. Some remarks are also given for an infinite mixture of Erlangs, in particular with regard to stochastic order properties.

Keywords:

• Erlang distribution
• mixture distributions
• failure rate
• stochastic order
• Descartes’ rule of signs