Ranlip generates random variates with an arbitrary multivariate lipschitz density.

while generation of random numbers from a variety of distributions is implemented in many packages (like gsl library http://www.gnu.org/software/gsl/ and unuran library http://statistik.wu-wien.ac.at/unuran/), generation of random variate with an arbitrary distribution, especially in the multivariate case, is a very challenging task. ranlip is a method of generation of random variates with arbitrary lipschitz-continuous densities, which works in the univariate and multivariate cases, if the dimension is not very large (say 3-10 variables).

lipschitz condition implies that the rate of change of the function (in this case, probability density p(x)) is bounded:

|p(x)-p(y)|
from this condition, we can build an overestimate of the density, so called hat function h(x)>=p(x), using a number of values of p(x) at some points. the more values we use, the better is the hat function. the method of acceptance/rejection then works as follows: generatea random variate x with density h(x); generate an independent uniform on (0,1) random number z; if p(x)<=z h(x), then return x, otherwise repeat all the above steps.

ranlip constructs a piecewise constant hat function of the required density p(x) by subdividing the domain of p (an n-dimensional rectangle) into many smaller rectangles, and computes the upper bound on p(x) within each of these rectangles, and uses this upper bound as the value of the hat function.