A new model for describing remission times: the generalized beta-generated Lindley distribution

Abstract

New generators are required to define wider distributions for modeling real data in survival analysis. To that end we introduce the four-parameter generalized beta-generated Lindley distribution. It has explicit expressions for the ordinary and incomplete moments, mean deviations, generating and quantile functions. We propose a maximum likelihood procedure to estimate the model parameters, which is assessed through a Monte Carlo simulation study. We also derive an additional estimation scheme by means of least square between percentiles. The usefulness of the proposed distribution to describe remission times of cancer patients is illustrated by means of an application to real data.

Keywords

• GBG generator
• remission times
• Extended Lindley model
• quantile function
• Lambert function