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

• Published in: Journal of statistical computation and simulation Vol. 94; no. 9; pp. 1965 - 1996
• Main Authors: Khoshkhoo Amiri, Z., MirMostafaee, S.M.T.K.
• Format: Journal Article
• Language: English
• Published: Abingdon Taylor & Francis 12.06.2024; Taylor & Francis Ltd
• Subjects: Algorithms; Bayesian analysis; COVID-19 data; Estimates; inter-record times; Markov chain Monte Carlo simulation; Parameters; predictive distribution; Statistical inference; Two-parameter bathtub-shaped distribution
• ISSN: 0094-9655; 1563-5163
• DOI: 10.1080/00949655.2024.2310682

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.