Parametric Confidence Intervals for the Renewal Function Using Coupled Integral Equations

ABSTRACT

In this article parametric inference for the renewal function is considered. An algorithm is presented for computing parametric confidence intervals for the renewal function. The partial derivatives needed in this algorithm are obtained by solving certain integral equations. The validity of asymptotic confidence intervals is checked via numerical experiments.

Keywords:

• Integral equation
• Maximum likelihood estimation
• Parametric confidence interval
• Renewal function
• Stieltjes integral

Mathematics Subject Classification:

• 62N05