  For a portfolio of life insurance policies observed for a stated period of
time, e.g., one year, mortality is typically a rare event. When we examine the
outcome of dying or not from such portfolios, we have an imbalanced binary
response. The popular logistic and probit regression models can be
inappropriate for imbalanced binary response as model estimates may be biased,
and if not addressed properly, it can lead to serious adverse predictions. In
this paper, we propose the use of skewed link regression models (Generalized
Extreme Value, Weibull, and Fre\`chet link models) as more superior models to
handle imbalanced binary response. We adopt a fully Bayesian approach for the
generalized linear models (GLMs) under the proposed link functions to help
better explain the high skewness. To calibrate our proposed Bayesian models, we
use a real dataset of death claims experience drawn from a life insurance
company's portfolio. Bayesian estimates of parameters were obtained using the
Metropolis-Hastings algorithm and for Bayesian model selection and comparison,
the Deviance Information Criterion (DIC) statistic has been used. For our
mortality dataset, we find that these skewed link models are more superior than
the widely used binary models with standard link functions. We evaluate the
predictive power of the different underlying models by measuring and comparing
aggregated death counts and death benefits.
