RNGs for some distributions written in Lua, mostly as a first exercise in the language.

rng.lua

-- Some RNGs for getting to play with Lua.
--
-- Carlos Agarie <carlos@onox.com.br>
--
-- Public domain.

-- N(mean; std^2).
function gauss(mean, std)
  if std <= 0.0 then error("standard deviation must be positive!") end

  u1 = math.random()
  u2 = math.random()

  r = math.sqrt(-2.0 * math.log(u1))
  theta = 2.0 * math.pi * u2
  return mean + std * r * math.sin(theta)
end

-- This distribution models the time between events in a Poisson process.
function exponential(mean)
  if mean <= 0.0 then error("mean must be positive!") end

  return -mean * math.log(math.random())
end

-- This is a non-exponential type of distribution, one without a mean value.
function cauchy(median, scale)
  if scale <= 0.0 then error("scale must be positive!") end

  return median + scale * math.tan(math.pi * (math.random() - 0.5))
end