A Plug-in Estimator for the Mean Value Function of a Geometric Process with Exponential Distribution

PEKALP M. H., ÖZBEK L., AYDOĞDU H.

International Conference on Numerical Analysis and Applied Mathematics (ICNAAM), Rhodes, Greece, 23 - 28 September 2019, vol.2293 identifier identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 2293
  • Doi Number: 10.1063/5.0026574
  • City: Rhodes
  • Country: Greece
  • Ankara University Affiliated: Yes

Abstract

In this paper, the estimation problem of the mean value function of a geometric process (GP) is considered. After obtaining the estimator, we investigate unbiasedness, asymptotic unbiasedness and consistency properties. Furthermore, using a power series expansion for the mean value function of a GP obtained from the integral equation satisfied by this tlinction, a computation method for proposed estimator is given when the distribution of the first inter-renewal time has an exponential distribution. Finally, a simulation study is presented to evaluate the small sample performance of the estimator for different parameter values.