We study the Galactic distribution of \sim 10,000 Asymptotic Giant Branch ( AGB ) stars selected by IRAS colors and variability index .
The distance to each star is estimated by assuming a narrow luminosity function and a model-derived bolometric correction .
The characteristic AGB star luminosity , L _ { AGB } , is determined from the condition that the highest number density must coincide with the Galactic bulge .
Assuming a bulge distance of 8 kpc , we determine L _ { AGB } \sim 3,500 L _ { \odot } , in close agreement with values obtained for nearby AGB stars using the HIPPARCOS data .

We find that there are no statistically significant differences in the Galactic distribution of AGB stars with different IRAS colors , implying a universal density distribution .
The direct determination of this distribution shows that it is separable in the radial , R , and vertical , z , directions .
Perpendicular to the Galactic plane , the number density of AGB stars is well described by an exponential function with a vertical scale height of 300 pc .
In the radial direction the number density of AGB stars is constant up to R \sim 5 kpc , and then it decreases exponentially with a scale length of \sim 1.6 kpc .
This fall-off extends to at least 12 kpc , where the sample becomes too small .
The overall normalization implies that there are about 200,000 AGB stars in the Galaxy .

We estimate the [ 25 ] - [ 12 ] color distribution of AGB stars for an unbiased volume-limited sample .
By using a model-dependent transformation between the color and mass-loss rate , \dot { M } , we constrain the time dependence of \dot { M } .
The results suggest that for 10 ^ { -6 } M _ { \odot } yr ^ { -1 } < \hbox { $ \dot { M } $ } < 10 ^ { -5 } M _ { \odot } yr ^ { -1 } the mass-loss rate increases exponentially with time .
We find only marginal evidence that the mass-loss rate increases with stellar mass .