# Bug#249546: ITP: libranlip -- generates random variates with multivariate Lipschitz density

```Package: wnpp
Severity: wishlist

* Package name    : libranlip
Version         : 1.0
Upstream Author : Gleb Beliakov <gleb@deakin.edu.au>
* URL             : http://www.deakin.edu.au/~gleb/ranlip.html
Description     : generates random variates with multivariate Lipschitz density

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)|<M||x-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.

Anibal Monsalve Salazar
--
.''`.  Debian GNU/Linux      | Building 28C
: :' :  Free Operating System | Monash University VIC 3800, Australia
`. `'   http://debian.org/    | http://www-personal.monash.edu/~anibal/
`-                          |
```

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