  The luminosity function of short Gamma Ray Bursts (GRBs) is modelled by using
the available catalogue data of all short GRBs (sGRBs) detected till October,
2017. The luminosities are estimated via the `pseudo-redshifts' obtained from
the `Yonetoku correlation', assuming a standard delay distribution between the
cosmic star formation rate and the production rate of their progenitors. While
the simple powerlaw is ruled out to high confidence, the data is fit well both
by exponential cutoff powerlaw and broken powerlaw models. Using the derived
parameters of these models along with conservative values in the jet opening
angles seen from afterglow observations, the true rate of short GRBs are
derived. Assuming a short GRB is produced from each binary neutron star merger
(BNSM), the rate of gravitational wave (GW) detections from these mergers are
derived for the past, present and future configurations of the GW detector
networks. Stringent lower limits of $1.87 \pyr$ for the aLIGO-VIRGO, and $3.11
\pyr$ for the upcoming aLIGO-VIRGO-KAGRA-LIGO/India configurations are thus
derived for the BNSM rate at $68 \%$ confidence. The BNSM rates calculated from
this work and that independently inferred from the observation of the only
confirmed BNSM observed till date, are shown to have a mild tension; however
the scenario that all BNSMs produce sGRBs cannot be ruled out.
