Estimation of the mean value function for gamma trend renewal process

PEKALP M. H., Karaduman M. O., Aydogdu H.

COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, vol.51, no.6, pp.3441-3456, 2022 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 51 Issue: 6
  • Publication Date: 2022
  • Doi Number: 10.1080/03610918.2022.2039707
  • Journal Name: COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Applied Science & Technology Source, Business Source Elite, Business Source Premier, CAB Abstracts, Compendex, Computer & Applied Sciences, Veterinary Science Database, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.3441-3456
  • Keywords: Trend renewal process, Trend renewal function, Power-law intensity, Log-Linear intensity, Estimation, GEOMETRIC PROCESSES, NONPARAMETRIC-ESTIMATION, STATISTICAL-INFERENCE
  • Ankara University Affiliated: Yes

Abstract

In this study, we deal with the estimation problem of the trend renewal function which is given as the mean value function of the trend renewal process by assuming that the distribution function of the time-transformed random variables is a gamma distribution with the shape parameter alpha and the scale parameter beta. For this purpose, to begin with, we yield the calculation procedure for the trend renewal function by using the Riemann-Stieltjes method. Then, we estimate the model parameters of the trend renewal process. Based on these estimators, an estimator of the trend renewal function is proposed and consistency property of this estimator is investigated. A simulation study is performed to evaluate the performance of all the given estimators according to bias and mean square error criteria. Finally, the applicability of the estimation procedure is applied to two real data sets.