  We present an improved statistical fluctuation analysis for measurement
device independent quantum key distribution with three-intensity decoy-state
method. Taking the statistical fluctuations for different sources jointly, we
present more tightened formulas for some key quantities used in calculating the
secure final key. Numerical simulation shows that, given the total number of
pulses $10^{12}$, our method improves the key rate by about 97\% for a distance
of 50kms compared with the result given by Xu., et al. (Phys. Rev. A 89,
052333); and improves the key rate by $146\%$ for a distance of 100kms compared
with the result from full optimization of all parameters but treating the
statistical fluctuations traditionally, i.e., treating the fluctuations for
different sources separately.
