On Modeling Bivariate Left Censored Data using Reversed Hazard Rates

TL;DR

This paper introduces a new model for analyzing bivariate left-censored data using reversed hazard rates, accounting for dependence between components, with estimation methods and real data applications.

Contribution

It proposes a novel dependence model based on vector reversed hazard rates for left-censored bivariate data, including estimation techniques and practical implementation.

Findings

Maximum likelihood estimation performs well for moderate sample sizes.

Bayesian estimation via Metropolis-Hastings is effective for complex likelihoods.

The model successfully analyzes real-world left-censored bivariate data.

Abstract

When the observations are not quantified and are known to be less than a threshold value, the concept of left censoring needs to be included in the analysis of such datasets. In many real multi component lifetime systems left censored data is very common. The usual assumption that components which are part of a system, work independently seems not appropriate in a number of applications. For instance it is more realistic to acknowledge that the working status of a component affects the remaining components. When you have left-censored data, it is more meaningful to use the reversed hazard rate, proposed as a dual to the hazard rate. In this paper, we propose a model for left-censored bivariate data incorporating the dependence enjoyed among the components, based on a dynamic bivariate vector reversed hazard rate proposed in Gurler (1996). The properties of the proposed model is studied. The maximum likelihood method of estimation is shown to work well for moderately large samples. The Bayesian approach to the estimation of parameters is also presented. The complexity of the likelihood function is handled through the Metropolis - Hastings algorithm. This is executed with the MH adaptive package in r. Different interval estimation techniques of the parameters are also considered. Applications of this model is demonstrated by illustrating the usefulness of the model in analyzing real data.