On adaptive progressive hybrid censored Burr type III distribution: application to the nano droplet dispersion data

ABSTRACT

In the current paper, the maximum likelihood and Bayes estimators for the two shape parameters of the Burr Type III distribution are investigated based on adaptive Type II progressive hybrid censored data. The maximum likelihood estimators are provided for estimating the unknown parameters. The existence and uniqueness of the maximum likelihood estimation are shown using the graphical method. The Bayes estimates are obtained under two loss functions using the Lindley’s method and Metropolis-Hastings sampling procedure. Further, approximate and Bayesian intervals are constructed. Monte Carlo simulation study is performed to check the accuracy of the estimates and compare the performance of the proposed confidence intervals. Also, the nano droplet data is analyzed to illustrate the application and development of the inference methods.

KEYWORDS:

• Adaptive Type II progressive hybrid censoring
• Burr type III
• interval estimation
• likelihood inference
• metropolis-hastings algorithm
• nano droplet dispersion

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Notes on contributors

Hanieh Panahi

Dr. Hanieh Panahi is an Assistant Professor in the Department of Mathematics and Statistics, Lahijan Branch, Islamic Azad University, Lahijan, Iran. Her main research interests include censored data, survival analysis, mathematical statistics, and applied Statistics.

Saeid Asadi

Dr. Saeid Asadi is an Associate Professor in the Department of Mechanical Engineering, Payame Noor university, Tehran, Iran. His research interests include nano and micro scale simulation and reliability model.