| Abstract: | The covariance of the number of renewals in a fixed time N t and the ensuing excess life time Y t is derived using matrix-analytic methods for the stationary PH-renewal process. Specific results for the Erlang and hyperexponential processes are provided to illustrate the ease of computation. Properties concerning the sign and the behavior of the covariance as t→∞ are provided throughout. Parameter estimation for renewal processes which cannot be fully observed serves as the motivation for our derivations. These statistical applications as well as links to estimation for service time distributions in queues shed light on the type of problems for which the covariance is useful. |
