Programs for the Landau and the Vavilov distributions and the corresponding random numbers

The Landau and the Vavilov distributions are used to describe the energy loss of charged particles traversing a thin layer of matter. For Monto Carlo simulations it is of particular interest to have a random number generator for these distributions. Fourier series are used to approximate the probability density functions, the cumulative distribution functions and the inverses of the conditional distribution functions. Theoretical considerations, together with numerical tests, show that in the case of the densities and the distribution functions three to five significant digits are obtained. In the case of the inverses of the conditional distribution functions three significant figures are obtained almost everywhere, except near the end points of the interval, where a relative error of up to 5-6% may sometimes occur.