Probing Cosmic Acceleration by Using Model-Independent Parametrizations
  and Three Kinds of Supernova Statistics Techniques
  In this work, we explore the evolution of the dark energy equation of state
{\omega} by using Chevalliear-PolarskiLinder (CPL) parametrization and the
binned parametrizations. For binned parametrizations, we adopt three methods to
choose the redshift interval: I. Ensure that "{\Delta}z = const", where
{\Delta}z is the width of each bin; II.Ensure that "n{\Delta}z = const", where
n is the number of SNIa in each bin; III. Treat redshift discontinuity points
as models parameters, i.e. "free {\Delta}z". For observational data, we adopt
JLA type Ia supernova (SNIa) samples, SDSS DR12 data, and Planck 2015 distance
priors. In particular, for JLA SNIa samples, we consider three statistic
techniques: I. Magnitude statistics, which is the traditional method; II. Flux
statistics, which reduces the systematic uncertainties of SNIa; III. Improve
flux statistics, which can reduce the systematic uncertainties and give tighter
constrains at the same time. The results are as follows: (1) For all the cases,
{\omega} = -1 is always satisfied at 1{\sigma} confidence regions; It means
that {\Lambda}CDM is still favored by current observations. (2) For magnitude
statistics, "free {\Delta}z" model will give the smallest error bars; this
conclusion does not hold true for flux statistics and improved flux statistic.
(3) The improved flux statistic yields a largest present fractional density of
matter {\Omega}m; in addition, this technique will give a largest current
deceleration parameter q0 , which reveals a universe with a slowest cosmic
acceleration.
