Discriminating between some lifetime distributions in geometric counting processes

Abstract

Gamma, lognormal and Weibull distributions are most commonly used in modeling asymmetric data coming from the areas of life testing and reliability engineering. In this study, we deal with the problem of selecting one of these distributions for a given data set which is consistent with the geometric process (GP) model according to $T$-statistic based on the ratio of the maximized likelihood (RML). First, we show that $T$-statistic performs better than Kolmogorov- Smirnov (KS), mean square error (MSE) and maximum percentage error (MPE) based on extensive simulation study. Then, by using the T-statistic, we determine the distributions of ten real data sets shown to be consistent with the GP model by Lam et al. (2004). After validating the distribution for these data sets, we calculate the estimators of the parameters by using the suitable method given in Lam and Chan (1998), Chan, Lam, and Leung (2004) or Aydoğdu, Şenoğlu, and Kara (2010). Then, we plot observed and the fitted values of the interarrival and arrival times for comparison.

Keywords:

• Geometric counting process
• Maximum likelihood estimation
• Modified maximum likelihood estimation
• Ratio of the maximized likelihood

Acknowledgments

The authors would like to thank the editor and anonymous referee(s) for their valuable and constructive comments and suggestions.

Disclosure statement

The authors declare that they have no conflict of interest.

Additional information

Funding

This study was supported by a research grant from Erasmus + Student Mobility for Traineeships.