In this study we propose two kinds of regression methods, there are proportional median reversed residual life model and accelerated median reversed residual life model.

- The proportional median residual life model is a functional analog to the Cox proportional hazards model. It assumes the constant proportionality of reversed median residual life function (RMRL) functions over the interval of interest. For this model we presented the non-parametric approach for parameter estimation, which required the minimization of the estimating function that is introduced. We set numerical studies to evaluate performance of the estimates. The bootstrap re-sampling technique was used to estimate the corresponding standard errors that can be used to obtain confidence intervals for parameters of performing hypothesis testing.
- The accelerated median reversed residual life model is the method that used for analytic the forms of resembles by accelerated failure time model. For this model we presented two methods of estimation – parametric and non-parametric under the accelerated failure time assumption. We set numerical studies to evaluate the performance of the regression coefficient estimate under the parametric assumption.