  Age of information (AoI) is an effective measure to quantify the information
freshness in wireless status update systems. It has been further validated that
the peak AoI has the potential to capture the core characteristics of the aging
process, and thus the average peak AoI is widely used to evaluate the long-term
performance of information freshness. However, the average peak AoI is a
risk-insensitive metric and therefore may not be well suited for evaluating
critical status update services. Motivated by this concern, and following the
spirit of entropic value-at-risk (EVaR) in the field of risk analysis, in this
paper we present a concept, termed Statistical AoI, for providing a unified
framework to guarantee various requirements of risk-sensitive status-update
services with the demand on the violation probability of the peak age. In
particular, as the constraint on the violation probability of the peak age
varies from loose to strict, the statistical AoI evolves from the average peak
AoI to the maximum peak AoI. We then investigate the statistical AoI
minimization problem for status updates over wireless fading channels. It is
interesting to note that the corresponding optimal sampling scheme varies from
step to constant functions of the channel power gain with the peak age
violation probability from one to zero. We also address the maximum statistical
AoI minimization problem for multi-status updates with time division multiple
access (TDMA), where longer transmission time can improve reliability but may
also cause the larger age. By solving this problem, we derive the optimal
transmission time allocation scheme. Numerical results show that our proposals
can better satisfy the diverse requirements of various risk-sensitive status
update services, and demonstrate the great potential of improving information
freshness compared to baseline approaches.
