# The QUANTLIFE Procedure

### Relationship of Quantile Function and Survival Function

Both quantile function and survival function are useful in characterizing a lifetime distribution.

By the definition of the quantile function ,

In other words, the cumulative distribution function maps to , and thus the corresponding survival function maps to .

When you specify the LOG option, the QUANTLIFE procedure fits a linear quantile regression model for a log transformation of the lifetime as

where is the th quantile of at x. The estimated quantile function for given x is , because the quantile function is invariant under a monotone transformation.

You can specify the covariates x in the COVARIATES= data set of the BASELINE statement and the PLOTS=(QUANTILE SURVIVAL) option in the PROC statement. Then the conditional quantile function at x is plotted as against , and the conditional survival function at x is plotted as against .