We have explored the use of maximum likelihood estimation techniques in the use of globular cluster luminosity functions (LFs) as distance indicators. In particular, we have tested size-of-sample effects through the analysis of Monte Carlo simulations of LFs drawn from an assumed universal population like that characterizing the globular clusters in the Local Group. Our working assumption, following others before us, is that the underlying LF is adequately well described by a Gaussian normal in a number vs. absolute magnitude representation.
For typically observable sample sizes in studies which are limited to the bright half of the LF, statistical limitations preclude a precise determination of the attributes which fully describe the LF, even in the absence of field object contamination. In particular, the intrinsic dispersion (the shape parameter of the LF) must be taken to be a universal constant, independent of galaxy type; only then may the turnover magnitude (which contains the distance information) be derived with good precision. Some data exist for nearby galaxies (including ellipticals) which permit an assessment of the universality of the intrinsic dispersion: they are not inconsistent with the hypothesis. However, it will be important to test this point in future as more data are secured.
Real globular clusters in remote galaxies are unresolved, and the samples are contaminated with foreground field stars and remote background objects. This contamination necessitates corrections which are statistical in nature, applicable to binned LFs. Through numerical simulations, we have tested the limitations imposed by realistic numbers of field objects in globular cluster LFs in remote galaxies, testing for systematic biases and assessing the attainable precision in derived distance as a function of the sample size and the limiting magnitude.