Calibration of RAVE distances with Hipparcos

I give treatments for a number of types of bias affecting calculation, including bias from the non-linear relationship between the quantity of interest (e.g., distance or distance modulus) and the measured quantity (parallax or visual magnitude), the Lutz-Kelker bias, and bias due to variation in density of the stellar population.

The use of a magnitude bound minimises the Malmquist and the Lutz-Kelker bias, and avoids a measurement bias because Hipparcos parallaxes are more accurate for brighter stars. The calibration is applicable to stars in 2MASS when there is some way to determine stellar class with reasonable confidence. For RAVE this is possible for hot dwarfs and using log g.