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Maps of the peculiar velocity field derived from distance relations areaffected by Malmquist type bias and selection effects. Because of the largenumber of interdependent effects, they are in most cases difficult to treatanalytically. Monte Carlo simulations are used to understand and evaluate theseeffects. In these simulations the ``true'' spatial distribution and relevantproperties of galaxies as well as selection effects and observationaluncertainties are realistically modeled. The results of the simulation candirectly be applied to correct observed peculiar velocity maps. The simulationis used to investigate biases in samples of measured peculiar velocities byLynden-Bell et al. (1988), Willick (1990) and the new sample of spiral galaxiesby Haynes et al. (1993). Based on the results obtained from the application ofour method to toy models we find that the method is a useful tool to estimatethe bias induced both by inhomogeneities and selection effects. This is acrucial step for the analysis of the Haynes \etal sample which was selectedwith a redshift dependent criterion.Comment: accepted for publication in The Astronomical Journal, LaTex file  using aaspptwo.sty macros, 18 pages + 15 figures, figures not included. A  postscript version including all figures can be obtained from  ftp://ecf.hq.eso.org/pub/preprints/malmquist.ps (2.8 MByte or 0.9 Mbyte for  the compressed version

Determination of Malmquist Bias and Selection Effects from Monte Carlo Simulations