We examine statistical methods for calibrating trigonometric parallaxes to retrieve the absolute magnitudes of stars, using Monte Carlo simulations. Here we consider the case of the zero-point of the period-luminosity relation for Cepheid variables. The method originally proposed by Ratnatunga & Casertano was revisited by introducing a realistic density distribution of sample stars belonging to the catalogue through prior calculations of the photometric distance for each star. It is found that our method gives an unbiased estimate, regardless of any dispersions in their absolute magnitude. We further investigate the reliability of results which depend on the accuracy of parallax. Our finding is that the accuracy ($\sim$1 mas) of Hipparcos parallaxes is not enough to obtain a reliable result due to a large variation among different ensembles of stars. More precise determination of parallaxes to an accuracy of 200 $\mu$as at least, which will be easily realized by the ongoing astrometric space satellites, will give a precise zero-point together with a dispersion in absolute magnitude.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html