New closed-form efficient estimators for a bivariate Weibull distribution

Abstract

This study aimed to develop new closed-form and efficient estimators for the parameters of the bivariate Weibull distribution. New estimators can be produced using closed-form $\sqrt{n}$-consistent estimators for all parameters, except for the association parameter for which the estimator is not in closed form. This is carried out by utilizing a theorem that produces asymptotically efficient estimators. To achieve this, $\sqrt{n}$-consistent estimators are introduced. Fisher observed and expected information matrices are derived and used to develop new estimators. A simulation study and real data application are included to validate the new estimators. Given that the new estimators are as asymptotically efficient as maximum likelihood estimators and are in closed form, except for the association parameter, they can be used effectively in state-space modelling or real-time processing models. This is because of the shorter computing time associated with them than with maximum likelihood estimators.

Keywords:

• Closed-form estimator
• efficient estimator
• maximum likelihood estimator
• real-time processing model

Disclosure statement

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

Additional information

Funding

The first author's research was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Education (2018R1D1A1B07045603) and the National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (2021R1A4A5032622).