  Gamma ray bursts have been divided into two classes, long-soft gamma ray
burst and short-hard gamma ray burst according to the bimodal distribution in
duration time. Due to the harder spectrum and the lack of afterglows of
short-hard bursts in optical and radio observations, different progenitors for
short-hard bursts and long-soft bursts have been suggested. Based on the X-ray
afterglow observation and the cumulative red-shift distribution of short-hard
bursts, Nakar et al. (2006) found that the progenitors of short-hard bursts are
consistent with old populations, such as mergers of binary neutron stars.
Recently, the existence of two subclasses in long-soft bursts has been
suggested after considering multiple characteristics of gamma-ray bursts,
including fluences and the duration time. In this work, we extended the
analysis of cumulative red-shift distribution to two possible subclasses in
L-GRBs. We found that two possible subclass GRBs show different red-shift
distributions, especially for red-shifts z > 1. Our results indicate that the
accumulative red-shift distribution can be used as a tool to constrain the
progenitor characteristics of possible subclasses in L-GRBs.
