The inverse power Lindley distribution in the presence of left-censored data

ABSTRACT

In this study, classical and Bayesian inference methods are introduced to analyze lifetime data sets in the presence of left censoring considering two generalizations of the Lindley distribution: a first generalization proposed by Ghitany et al. [Power Lindley distribution and associated inference, Comput. Statist. Data Anal. 64 (2013), pp. 20–33], denoted as a power Lindley distribution and a second generalization proposed by Sharma et al. [The inverse Lindley distribution: A stress–strength reliability model with application to head and neck cancer data, J. Ind. Prod. Eng. 32 (2015), pp. 162–173], denoted as an inverse Lindley distribution. In our approach, we have used a distribution obtained from these two generalizations denoted as an inverse power Lindley distribution. A numerical illustration is presented considering a dataset of thyroglobulin levels present in a group of individuals with differentiated cancer of thyroid.

KEYWORDS:

• Lindley distribution
• likelihood
• Bayesian analysis
• survival analysis

Acknowledgments

The authors are grateful to Gabriel Sánchez Guzmán, a surgeon head and neck of the Clinica Cardio Infantil de Bogotá, who kindly provided the data set used to fit the models proposed in our methodology. The third author had partial financial support by the Coordenação de Aperfeiçoamento de pessoal de Nível superior (CAPES) of Brazil. We would like to thank the Editor-in-Chief, Associate Editor and two referees for careful reading and for comments which greatly improved the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.