  Supernova explosion and the associated neutron star natal kicks are important
events on a pathway of a binary to become a gravitational wave source, an X-ray
binary or a millisecond radio pulsar. Weak natal kicks often lead to binary
survival, while strong kicks frequently disrupt the binary. In this article, we
aim to further constrain neutron star natal kicks in binaries. We explore
binary population synthesis models by varying prescription for natal kick,
remnant mass and mass accretion efficiency. We introduce a robust statistical
technique to analyse combined observations of different nature. Using this
technique, we further test different models using parallax and proper motion
measurements for young isolated radio pulsars and similar measurements for
Galactic Be X-ray binaries. Our best model for natal kicks is consistent with
both measurements and contains a fraction of $w=0.2\pm 0.1$ weak natal kicks
with $\sigma_1 = 45^{+25}_{-15}$ km/s, the remaining natal kicks are drawn from
the high-velocity component, same as in previous works: $\sigma_2 = 336$ km/s.
We found that currently used models for natal kicks of neutron stars produced
by electron capture supernova (combination of maxwellian $\sigma=265$ km/s and
$\sigma = 30$ km/s for electron capture) are inconsistent or marginally
consistent with parallaxes and proper motions measured for isolated radio
pulsars. We suggest a new model for natal kicks of ecSN, which satisfy both
observations of isolated radio pulsars and Be X-ray binaries.

High Energy Astrophysical Phenomena;Solar and Stellar Astrophysics