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I present an analysis for fitting cosmological parameters from a HubbleDiagram of a standard candle with unknown intrinsic magnitude dispersion. Thedispersion is determined from the data themselves, simultaneously with thecosmological parameters. This contrasts with the strategies used to date. Theadvantages of the presented analysis are that it is done in a single fit (it isnot iterative), it provides a statistically founded and unbiased estimate ofthe intrinsic dispersion, and its cosmological-parameter uncertainties accountfor the intrinsic dispersion uncertainty. Applied to Type Ia supernovae, mystrategy provides a statistical measure to test for sub-types and assess thesignificance of any magnitude corrections applied to the calibrated candle.Parameter bias and differences between likelihood distributions produced by thepresented and currently-used fitters are negligibly small for existing andprojected supernova data sets.

Type Ia Supernova Intrinsic Magnitude Dispersion and the Fitting of Cosmological Parameters