Using available infrared photometry and the period-infrared luminosity relationship, we have analyzed a nearly complete sample of oxygen-rich Miras at Galactic latitudes with \b\ > 30-degrees. In agreement with previous kinematic studies, we find a marked difference in the spatial distributions between the stars with periods less than and those with periods greater than 300 days. For the stars with 300 > P < 400 days (our "intermediate"-period Miras), the exponential scale height from the Galactic plane is close to 240 pc, the projected surface density is approximately 100 kpc-2, and the local space density is approximately 210 kpc-3. Those stars with periods less than 300 days (our "short"-period Miras) can have their distance from the Galactic plane modeled by an exponential with a scale height of between 500 and 600 pc, depending upon the zero point of the period-luminosity relationship, which is probably metallicity dependent. These short-period Miras do not belong to the standard "thin disk" population which has a maximum exponential scale height of approximately 300 pc. The surface density projected onto the Galactic plane of these short-period Miras is between 40 and 60 kpc-2, and the space density in the Galactic plane is between 35 and 60 kpc-3. The progenitors of the Miras with P > 300 days appear to be disk dwarfs with typical main-sequence masses of between 1.0 and 1.2 M.. The masses of main-sequence progenitors of the short-period Miras are 1.1 M. or less. A typical mass for the main-sequence progenitors of less than 1 M. would indicate an age greater than 10(10) yr for these stars; this result would pose a severe difficulty for understanding the white dwarf luminosity function since it would produce many more old white dwarfs with luminosities of less than 10(-4) L. than are observed. Because they exhibit significant amounts of circumstellar dust, we estimate that the metallicity of the short-period Miras is at least one-third of the standard solar value. We estimate a duration of the Mira phase for the intermediate-period stars to be approximately 2 x 10(5) yr, somewhat longer than other recent estimates. Both short- and intermediate-period oxygen-rich Miras characteristically lose mass at approximately 10(-7) M. yr-1.
