  I present an analysis for fitting cosmological parameters from a Hubble
Diagram of a standard candle with unknown intrinsic magnitude dispersion. The
dispersion is determined from the data themselves, simultaneously with the
cosmological parameters. This contrasts with the strategies used to date. The
advantages of the presented analysis are that it is done in a single fit (it is
not iterative), it provides a statistically founded and unbiased estimate of
the intrinsic dispersion, and its cosmological-parameter uncertainties account
for the intrinsic dispersion uncertainty. Applied to Type Ia supernovae, my
strategy provides a statistical measure to test for sub-types and assess the
significance of any magnitude corrections applied to the calibrated candle.
Parameter bias and differences between likelihood distributions produced by the
presented and currently-used fitters are negligibly small for existing and
projected supernova data sets.
