D. H. Kelker coauthored the classical Lutz-Kelker bias analysis with T. E. Lutz. Its mathematical question is how a noisy observed stellar parallax, together with assumptions about the underlying stellar population, changes the inference of absolute magnitude.
The paper makes those assumptions explicit, including a Gaussian distribution for measurement errors. Its correction belongs to that statistical model; applying it to a different selection process requires checking the model again.[ref]
On the Use of Trigonometric Parallaxes for the Calibration of Luminosity Systems: Theory by T. E. Lutz and D. H. Kelker. pp. 573–574, abstract and beginning of The Distribution Function
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