Statistical inference for a two-parameter distribution with a bathtub-shaped or increasing hazard rate function based on record values and inter-record times with an application to COVID-19 data

Abstract

In this paper, we study the problem of estimation and prediction for a two-parameter distribution with a bathtub-shaped or increasing failure rate function based on lower records and inter-record times, and based on lower records without considering the inter-record times. The maximum likelihood and Bayesian approaches are employed to estimate the unknown parameters. As it seems that the Bayes estimates cannot be derived in a closed form, the Metropolis-Hastings within Gibbs algorithm is implemented to obtain the approximate Bayes point estimates. Bayesian prediction of a future record value is also discussed. A simulation study is conducted to evaluate the proposed point and interval estimators. A real data set consisting of COVID-19 data from Iran is analyzed to illustrate the application of the theoretical results of the paper. Moreover, a simulated data example is presented. Several concluding remarks end the paper.

Keywords:

• Two-parameter bathtub-shaped distribution
• inter-record times
• predictive distribution
• COVID-19 data
• Markov chain Monte Carlo simulation

Acknowledgments

We would like to thank the referees for their valuable comments which led to an improved version of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).