Modified Median Statistics and Type Ia Supernova Data

Abstract

The median statistic has recently been discussed by Gott \textit{et al.} as a more reliable alternative to the standard $χ^2$ likelihood analysis, in the sense of requiring fewer assumptions about the data and being almost as constraining. We apply this statistic to the currently available combined dataset of 92 distant type Ia supernovae, and also to a mock SNAP-class dataset. We find that the performances of the modified median and $χ^2$ statistics are comparable, particularly in the latter case. We further extend the work of Gott \textit{et al.} by modifying the median statistic to account for the number and size of sequences of consecutive points above or below the median. We also comment on how the performance of the statistic depends on the choice of free parameters that one is estimating.