Estimation of the generalized exponential renewal function

Abstract

When the shape parameter is a non-integer of the generalized exponential (GE) distribution, the analytical renewal function (RF) usually is not tractable. To overcome this, the approximation method has been used in this paper. In the proposed model, the n-fold convolution of the GE cumulative distribution function (CDF) is approximated by n-fold convolutions of gamma and normal CDFs. We obtain the GE RF by a series approximation model. The method is very simple in the computation. Numerical examples have shown that the approximate models are accurate and robust. When the parameters are unknown, we present the asymptotic confidence interval of the RF. The validity of the asymptotic confidence interval is checked via numerical experiments.

Keywords:

• renewal function
• GE distribution
• gamma distribution
• normal distribution
• series truncation approximation
• parametric confidence interval

View correction statement:

Estimation of the generalized exponential renewal function

Acknowledgements

The authors are very grateful to the editor and the referees for constructive comments and suggestions. This work was supported by the National Natural Science Foundation of China (71171103) and Specialized Research Fund for the Doctoral Program of Zhanjiang Normal University (ZL1102).