  The energy coupling efficiency of active galactic nucleus (AGN) outbursts is
known to differ significantly with factors including the jet kinetic power,
duration of the outburst, and properties of the host galaxy cluster. As such,
constraints on their jet power and lifetime functions are crucial to quantify
the role of kinetic-mode AGN feedback on the evolution of galaxies since $z
\sim 1$. In this work, we address this issue by measuring the energetics of a
sample of 79 low-redshift (0.02 $< z <$ 0.2) remnant radio galaxies compiled
from large-sky radio surveys - these objects uniquely probe the full duration
of an AGN outburst. The jet kinetic power and outburst duration of each remnant
are determined using the RAiSE dynamical model based on the surface brightness
distribution observed in multi-frequency radio images. We compare the
energetics constrained for this sample to those predicted for mock radio source
populations - with various intrinsic functions for jet power and lifetime
distributions - to correct for sample selection biases imposed on our sample.
The intrinsic jet power and lifetime functions that yield a selection-biased
mock population most similar to our observed sample are found using Bayesian
inference. Our analysis places robust constraints on assumed power-law indices
for the intrinsic jet power and lifetime functions: $p(Q)\propto
Q^{-1.49\pm0.07}$ and $p(t_{\mathrm{on}})\propto
t_{\mathrm{on}}^{-0.97\pm0.12}$ respectively. We discuss the implication of
these findings for feedback-regulated accretion and the self-regulating nature
of jet activity. The methodology proposed in this work can be extended to
active radio galaxies in future studies.
