  Numerical procedures to generate random variates that follow loss-cone
velocity distributions in particle simulations are presented. We propose a
simple summation algorithm for the Ashour-Abdalla--Kennel-type loss-cone
distribution, also known as the subtracted Maxwellian. For the Dory-type
loss-cone distribution, we use a random variate for the gamma distribution.
Extending earlier algorithms for the kappa and Dory-type distributions, we
construct a novel algorithm to generate a popular form of a kappa loss-cone
distribution. To better express the loss cone, we discuss another family of
loss-cone distributions based on the pitch angle. In addition to the
acceptance-rejection method, we propose two transformation algorithms that
convert an isotropic distribution into a loss-cone distribution. This allows us
to generate loss-cone and kappa loss-cone distributions from the Maxwell and
kappa distributions.
