The observed isotropy on the sky and non-uniform spatial
distribution of GRB revealed by the BATSE device onboard the Compton
Gamma-Ray Observatory (e.g. Meegan et al. 1992) lend support to the idea
of cosmological origin of GRB (Prilutski & Usov 1975; Usov &
Chibisov 1975) for which the best candidates could be merging
binary NS+NS or NS+BH at high redshifts ( 
),
(Blinnikov, et al. 1984; Paczynski 1991, 1992). Narayan, Paczynski & Piran
(1992) argued that the rate of double NS coalescence as a result
of orbital shrinking induced by gravitational waves are far from
being sufficient to explain the observed properties of cosmic
GRB and their rate ( 
bursts per day). Wickramasinghe
et al (1993) showed the consistency of standard cosmology and
the BATSE GRB 
- 
distribution.
The cosmological models for GRB have not yet been proven; moreover, they come across severe problems (such as no-host-galaxy limits, baryon contamination degradation of the high energy photons, efficiency problems at getting the NS binding energy out of the BH into gamma-rays etc.), which we will not address here.
However, the cosmological models involving binary NS or NS+BH
coalescences must have clear observational consequences in showing the
effects of binary coalescence rate evolution on the observed -
distribution and 
. Attempts to take the intrinsic evolution of the
sources into account have been carried out in a number of papers (see
e.g. Piran 1992; Yi 1994; Cohen & Piran 1995), but all of them used
simple ad hoc assumptions for the sources evolution.
Both the parameters of the cosmological model and source evolution are known to influence the shape of the integral statistical distributions of sources (e.g. Weinberg 1972), and it has until now been very difficult or even impossible to separate these effects from each other. This is similar to the failure of using counts of radio sources to check the cosmological models, as the evolution of number per comoving frame, spectral shape, luminosity etc is very complicated and poorly understood as yet.
In contrast, the evolution of binary systems being based and confirmed
by a bulk of astronomical observations at different wavelengths is much
better understood. The analysis of the evolutionary scenario of
binary systems by Lipunov et al. 1995 showed that a few key parameters
largely define the overall binary evolution. These parameters are the
spectrum f(q) of the initial binary mass ratio 
and
the efficiency 
of binary orbital momentum transfer into a
common envelope. These parameters can be constrained by comparing
the numbers of binaries in different stages of evolution in the Galaxy
predicted by the scenario with the observed numbers (Lipunov et al. 1995).
In the present paper we compute the cumulative statistical
distribution, - , and test for binary NS and NS+BH coalescence
taking into account the temporal change of their rates
found by Monte-Carlo modelling of the modern scenario of binary
star evolution (the ``Scenario Machine'' method). A comparison
of the computed distribution with that of the 2nd BATSE GRB
catalogue (Meegan et al. 1994) is also made.