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abstract: 'By using the Sloan Digital Sky Survey (SDSS) first year type Ia supernova (SN Ia) compilation, we compare two different approaches (traditional $\chi^2$ and complete likelihood) to determine parameter constraints when the magnitude dispersion is to be estimated as well. We consider cosmological constant + Cold Dark Matter ($\Lambda$CDM) and spatially flat, constant $w$ Dark Energy + Cold Dark Matter (F$w$CDM) cosmological models and show that, for current data, there is a small difference in the best fit values and $\sim$ 30% difference in confidence contour areas in case the MLCS2k2 light-curve fitter is adopted. For the SALT2 light-curve fitter the differences are less significant ($\lesssim 13\%$ difference in areas). In both cases the likelihood approach gives more restrictive constraints. We argue for the importance of using the complete likelihood instead of the $\chi^2$ approach when dealing with parameters in the expression for the variance.'
author:
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    Bruno L. Lago[^1] [^2], Maurício O. Calvão[^3], Sérgio E. Jorás[^4],\
    Ribamar R. R. Reis[^5], Ioav Waga[^6] and Ramón Giostri[^7]   [^8]\
    *Instituto de Física, Universidade Federal do Rio de Janeiro,*\
    *C. P. 68528, CEP 21941-972, Rio de Janeiro, RJ, Brasil*
title: 'Type Ia supernova parameter estimation: a comparison of two approaches 