  Two different luminosity indicators have recently been proposed for Gamma Ray
Bursts that use gamma-ray observations alone. They relate the burst luminosity
(L) with the time lag between peaks in hard and soft energies, and the
spikiness or variability of the burst's light curve (V). These relations are
currently justified and calibrated with only 6 or 7 bursts with known red
shifts. We have examined BATSE data for the lag and V for 112 bursts. (1) A
strong correlation between the lag and V exists, and it is exactly as predicted
from the two proposed relations. This is proof that both luminosity indicators
are reliable. (2) GRB830801 is the all-time brightest burst, yet with a small V
and a large lag, and hence is likely the closest known event being perhaps as
close as 3.2 Mpc. (3) We have combined the luminosities as derived from both
indicators as a means to improve the statistical and systematic accuracy when
compared with the accuracy from either method alone. The result is a list of
112 bursts with good luminosities and hence red shifts. (4) The burst averaged
hardness ratio rises strongly with the luminosity of the burst. (5) The burst
luminosity function is a broken power law, with the break at L = 2x10^{52}
erg/s. The luminosity function has power law indices of -2.8+-0.2 above the
break and -1.7+-0.1 below the break. (6) The number density of GRBs varies with
red shift roughly as (1+z)^(2.5+-0.3) between 0.2<z<5. Excitingly, this result
also provides a measure of the star formation rate out to z~5 with no effects
from reddening, and the rate is rising uniformly for red shifts above 2.
