  This article analyzes the problem of estimating the time until an event
occurs, also known as survival modeling. We observe through substantial
experiments on large real-world datasets and use-cases that populations are
largely heterogeneous. Sub-populations have different mean and variance in
their survival rates requiring flexible models that capture heterogeneity. We
leverage a classical extension of the logistic function into the survival
setting to characterize unobserved heterogeneity using the beta distribution.
This yields insights into the geometry of the problem as well as efficient
estimation methods for linear, tree and neural network models that adjust the
beta distribution based on observed covariates. We also show that the
additional information captured by the beta distribution leads to interesting
ranking implications as we determine who is most-at-risk. We show theoretically
that the ranking is variable as we forecast forward in time and prove that
pairwise comparisons of survival remain transitive. Empirical results using
large-scale datasets across two use-cases (online conversions and retention
modeling), demonstrate the competitiveness of the method. The simplicity of the
method and its ability to capture skew in the data makes it a viable
alternative to standard techniques particularly when we are interested in the
time to event and when the underlying probabilities are heterogeneous.
